Document Zbl 1521.05159

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1521.05159 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1521.05159?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1521.05159" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/hu.jie" title="Author Profile">Hu, Jie</a>; <a href="/authors/li.hao" title="Author Profile">Li, Hao</a>; <a href="/authors/wang.yue.9" title="Author Profile">Wang, Yue</a>; <a href="/authors/yang.donglei" title="Author Profile">Yang, Donglei</a></div> <h2 class="title"> <strong>Graph tilings in incompatibility systems.</strong> <i>(English)</i> <a class="label nowrap" href="/1521.05159">Zbl 1521.05159</a> </h2> <div class="source"> <a href="/serials/1220" title="Journal Profile">SIAM J. Discrete Math.</a> <a href="/?q=in%3A500874" title="Articles in this Issue">37, No. 3, 1930-1951 (2023)</a>. </div> <div class="abstract">Let $H$ and $G$ be two simple, finite, and undirected graphs. An $H$-tiling is a collection of vertex-disjoint copies of $H$ in $G$. An $H$-factor (or perfect $H$-tiling) is an $H$-tiling which covers all vertices of $G$. A significant result of <span class="zbmathjax-textit">D. Kühn</span> and <span class="zbmathjax-textit">D. Osthus</span> [Combinatorica 29, No. 1, 65–107 (2009; <a href="/1517.05143">Zbl 1517.05143</a>)] wants to characterize, up to an additive constant, the best possible minimum degree condition which forces an $H$-factor, as in the following theorem:<br class="zbmathjax-paragraph">Theorem. For any $H$ there exist integers $C =C(H)$ and $n_0 = n_0(H)$ such that every graph $G$ whose order $n \geq n_0$ is divisible by $|H|$ and whose minimum degree is at least $(1- 1/\chi^\ast (H))n +C$ contains an $H$-factor.<br class="zbmathjax-paragraph">There are several generalizations of the theorem above, more information can be found in [<span class="zbmathjax-textit">E. Hurley</span> et al., “Sufficient conditions for perfect mixed tilings”, Preprint, <a href="https://arxiv.org/abs/2201.03944">arXiv:2201.03944</a>; <span class="zbmathjax-textit">J. Hyde</span> and <span class="zbmathjax-textit">A. Treglown</span>, Electron. J. Comb. 27, No. 3, Research Paper P3.48, 30 p. (2020; <a href="/1442.05107">Zbl 1442.05107</a>); <span class="zbmathjax-textit">D. Kühn</span> et al., SIAM J. Discrete Math. 23, No. 3, 1335–1355 (2009; <a href="/1207.05059">Zbl 1207.05059</a>)]. <br class="zbmathjax-paragraph"><span class="zbmathjax-textit">M. Krivelevich</span> et al. [Combinatorica 37, No. 4, 697–732 (2017; <a href="/1399.05143">Zbl 1399.05143</a>)] studied the robustness of Hamiltonicity of Dirac graphs with respect to the incompatibility system, as in the following theorem:<br class="zbmathjax-paragraph">Theorem. There exists a constant $\mu > 0$ such that the following holds for large enough $n$. For every $n$-vertex Dirac graph $G$ and a $\mu n$-bounded incompatibility system $\mathcal{F}$ defined over $G$, there exists a compatible Hamilton cycle.<br class="zbmathjax-paragraph">The main aim of this work is to study a more general setting of incompatibility systems, which was first proposed by Krivelevich et al. [loc. cit.]. This paper has three interesting results and we list them as follows:<br class="zbmathjax-paragraph">Theorem 1.7. Let $h \in \mathbb{N}$ and $H$ be any $h$-vertex graph. For any $\alpha > 0$, there exists a constant $\mu > 0$ such that for any sufficiently large $n$ with $n \in h\mathbb{N}$, every $(n, 1-\frac{1}{\chi^\ast (H)} +\alpha ,\mu)$-incompatibility system $(G,\mathcal{F})$ contains a compatible $H$-factor. In particular, the term of $\alpha$ in the minimum degree condition cannot be omitted when $H$ is a complete $r$-partite graph for $r \geq 3$.<br class="zbmathjax-paragraph">Lemma 2.3 (absorbing lemma). Let $H$ be an $h$-vertex graph with $\chi(H) \geq 2$. For any $\alpha ,\sigma>0$, there exist $\mu , \xi> 0$ such that for any sufficiently large $n$, if $(G,\mathcal{F})$ is an $(n, 1-\frac{1}{\chi^\ast (H)} +\alpha ,\mu)$-incompatibility system, then $G$ contains a $\xi$-absorbing set $A$ of size at most $\sigma n$.<br class="zbmathjax-paragraph">Lemma 2.4 (almost cover). Let $H$ be an $h$-vertex graph with $\chi(H) \geq 2$. For any $\alpha , \tau> 0$, there exists $\mu > 0$ such that for any sufficiently large $n$, if $(G,\mathcal{F})$ is an $(n, 1-\frac{1}{\chi_{cr} (H)} +\alpha ,\mu)$-incompatibility system, then there exists a compatible $H$-tiling covering all but at most $\tau n$ vertices of $G$.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A20318">Mehrdad Nasernejad (Lens)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7734876">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C70" title="MSC2020">05C70</a> </td> <td class="space"> Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C35" title="MSC2020">05C35</a> </td> <td class="space"> Extremal problems in graph theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Agraph+tilings">graph tilings</a>; <a href="/?q=ut%3Aincompatibility+system">incompatibility system</a>; <a href="/?q=ut%3Arobustness">robustness</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1517.05143">Zbl 1517.05143</a>; <a href="/1442.05107">Zbl 1442.05107</a>; <a href="/1207.05059">Zbl 1207.05059</a>; <a href="/1399.05143">Zbl 1399.05143</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1521.05159" data-ciurl="/ci/07734876" data-biburl="/bibtex/07734876.bib" data-amsurl="/amsrefs/07734876.bib" data-xmlurl="/xml/07734876.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07734876.pdf" title="Zbl 1521.05159 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1137/22M1506353" aria-label="DOI for “Graph tilings in incompatibility systems”" title="10.1137/22M1506353">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2207.05386"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Alon, N. and Gutin, G., Properly colored Hamilton cycles in edge-colored complete graphs, Random Structures Algorithms, 11 (1997), pp. 179-186. · <a href="/0882.05084" class="nowrap">Zbl 0882.05084</a></td> </tr><tr> <td>[2]</td> <td class="space">Alon, N., Jiang, T., Miller, Z., and Pritikin, D., Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints, Random Structures Algorithms, 23 (2003), pp. 409-433. · <a href="/1037.05033" class="nowrap">Zbl 1037.05033</a></td> </tr><tr> <td>[3]</td> <td class="space">Alon, N. and Sudakov, B., Increasing the chromatic number of a random graph, J. Comb., 1 (2010), pp. 345-356. · <a href="/1244.05194" class="nowrap">Zbl 1244.05194</a></td> </tr><tr> <td>[4]</td> <td class="space">Alon, N. and Yuster, R., H-factors in dense graphs, J. Comb. Theory Ser. B, 66 (1996), pp. 269-282. · <a href="/0855.05085" class="nowrap">Zbl 0855.05085</a></td> </tr><tr> <td>[5]</td> <td class="space">Balogh, J., Csaba, B., and Samotij, W., Local resilience of almost spanning trees in random graphs, Random Structures Algorithms, 38 (2011), pp. 121-139. · <a href="/1215.05154" class="nowrap">Zbl 1215.05154</a></td> </tr><tr> <td>[6]</td> <td class="space">Beck, J., Random graphs and positional games on the complete graph, in Random Graphs ’83, , North-Holland, Amsterdam, (1985), pp. 7-13. · <a href="/0602.05046" class="nowrap">Zbl 0602.05046</a></td> </tr><tr> <td>[7]</td> <td class="space">Ben-Shimon, S., Krivelevich, M., and Sudakov, B., On the resilience of Hamiltonicity and optimal packing of Hamilton cycles in random graphs, SIAM J. Discrete Math., 25 (2011), pp. 1176-1193, doi:10.1137/110821299. · <a href="/1237.05187" class="nowrap">Zbl 1237.05187</a></td> </tr><tr> <td>[8]</td> <td class="space">Bollobás, B. and Erdős, P., Alternating Hamiltonian cycles, Isr. J. Math., 23 (1976), pp. 126-131. · <a href="/0325.05114" class="nowrap">Zbl 0325.05114</a></td> </tr><tr> <td>[9]</td> <td class="space">Bollobás, B. and Papaioannou, A., A biased Hamiltonian game, Congr. Numer., 35 (1982), pp. 105-115. · <a href="/0516.05035" class="nowrap">Zbl 0516.05035</a></td> </tr><tr> <td>[10]</td> <td class="space">Bondy, J., Paths and cycles, in Handbook of Combinatorics, Graham, R., Grotschel, M., and Lovász, L., eds., Vol. 1, 1995, pp. 5-110.</td> </tr><tr> <td>[11]</td> <td class="space">Chang, F., Han, J., Kim, J., Wang, G., and Yang, D., Embedding Clique-factors in Graphs with Low $\ell $ -independence Number, preprint, https://arxiv.org/abs/2111.10512, 2021. · <a href="/1512.05331" class="nowrap">Zbl 1512.05331</a></td> </tr><tr> <td>[12]</td> <td class="space">Chang, Y., Han, J., Kohayakawa, Y., Morris, P., and Mota, G. O., Factors in randomly perturbed hypergraphs, Random Structures Algorithms, 60 (2022), pp. 153-165. · <a href="/1522.05420" class="nowrap">Zbl 1522.05420</a></td> </tr><tr> <td>[13]</td> <td class="space">Chen, C. and Daykin, D. E., Graphs with Hamiltonian cycles having adjacent lines different colors, J. Combin. Theory, Ser. B, 21 (1976), pp. 135-139. · <a href="/0287.05106" class="nowrap">Zbl 0287.05106</a></td> </tr><tr> <td>[14]</td> <td class="space">Chvátal, V. and Erdős, P., Biased positional games, Ann. Discrete Math., 2 (1978), pp. 221-229. · <a href="/0374.90086" class="nowrap">Zbl 0374.90086</a></td> </tr><tr> <td>[15]</td> <td class="space">Cooley, O., Kühn, D., and Osthus, D., Perfect packings with complete graphs minus an edge, Eur. J. Combin., 28 (2007), pp. 2143-2155. · <a href="/1136.05055" class="nowrap">Zbl 1136.05055</a></td> </tr><tr> <td>[16]</td> <td class="space">Coulson, M., Keevash, P., Perarnau, G., and Yepremyan, L., Rainbow factors in hypergraphs, J. Combin. Theory Ser. A, 172 (2020), 105184. · <a href="/1433.05116" class="nowrap">Zbl 1433.05116</a></td> </tr><tr> <td>[17]</td> <td class="space">Coulson, M. and Perarnau, G., Rainbow matchings in Dirac bipartite graphs, Random Structures Algorithms, 55 (2019), pp. 271-289. · <a href="/1426.05137" class="nowrap">Zbl 1426.05137</a></td> </tr><tr> <td>[18]</td> <td class="space">Coulson, M. and Perarnau, G., A rainbow Dirac’s theorem, SIAM J. Discrete Math., 34 (2020), pp. 1670-1692, doi:10.1137/18M1218881. · <a href="/1450.05050" class="nowrap">Zbl 1450.05050</a></td> </tr><tr> <td>[19]</td> <td class="space">Dellamonica, D. Jr, Kohayakawa, Y., Marciniszyn, M., and Steger, A., On the resilience of long cycles in random graphs, Electron. J. Combin., 15 (2008), R32. · <a href="/1181.05053" class="nowrap">Zbl 1181.05053</a></td> </tr><tr> <td>[20]</td> <td class="space">Diestel, R., Extremal graph theory, in Graph Theory, Springer, 2017, pp. 173-207. · <a href="/1365.05001" class="nowrap">Zbl 1365.05001</a></td> </tr><tr> <td>[21]</td> <td class="space">Dirac, G. A., Some theorems on abstract graphs, Proc. Lond. Math. Soc., 3 (1952), pp. 69-81. · <a href="/0047.17001" class="nowrap">Zbl 0047.17001</a></td> </tr><tr> <td>[22]</td> <td class="space">Ehard, S., Glock, S., and Joos, F., A rainbow blow-up lemma for almost optimally bounded edge-colourings, Forum Math., Sigma, 8 (2020), E37, doi:10.1017/fms.2020.38. · <a href="/1473.05086" class="nowrap">Zbl 1473.05086</a></td> </tr><tr> <td>[23]</td> <td class="space">Erdős, P. and Spencer, J., Lopsided lovász local lemma and latin transversals, Discrete Appl. Math., 30 (1991), pp. 151-154. · <a href="/0717.05017" class="nowrap">Zbl 0717.05017</a></td> </tr><tr> <td>[24]</td> <td class="space">Glock, S. and Joos, F., A rainbow blow-up lemma, Random Structures Algorithms, 56 (2020), pp. 1031-1069, doi:10.1002/rsa.20907. · <a href="/1458.05067" class="nowrap">Zbl 1458.05067</a></td> </tr><tr> <td>[25]</td> <td class="space">Hajnal, A. and Szemerédi, E., Proof of a conjecture of P. Erdős, Combin. Theory Appl., 2 (1970), pp. 601-623. · <a href="/0217.02601" class="nowrap">Zbl 0217.02601</a></td> </tr><tr> <td>[26]</td> <td class="space">Han, J., Decision problem for perfect matchings in dense k-uniform hypergraphs, Trans. Amer. Math. Soc., 369 (2017), pp. 5197-5218, doi:10.1090/tran/6999. · <a href="/1359.05100" class="nowrap">Zbl 1359.05100</a></td> </tr><tr> <td>[27]</td> <td class="space">Han, J., Morris, P., Wang, G., and Yang, D., A Ramsey-Turán Theory for Tilings in Graphs, preprint, https://arxiv.org/abs/2106.09688, 2021.</td> </tr><tr> <td>[28]</td> <td class="space">Han, J., Zang, C., and Zhao, Y., Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs, J. Combin. Theory Ser. A, 149 (2017), pp. 115-147, doi:10.1016/j.jcta.2017.02.003. · <a href="/1358.05070" class="nowrap">Zbl 1358.05070</a></td> </tr><tr> <td>[29]</td> <td class="space">Hurley, E., Joos, F., and Lang, R., Sufficient Conditions for Perfect Mixed Tilings, preprint, https://arxiv.org/abs/2201.03944, 2022.</td> </tr><tr> <td>[30]</td> <td class="space">Hyde, J. and Treglown, A., A degree sequence version of the Kühn-Osthus tiling theorem, Electron. J. Combin., 27 (2020), 3.48. · <a href="/1442.05107" class="nowrap">Zbl 1442.05107</a></td> </tr><tr> <td>[31]</td> <td class="space">Kawarabayashi, K., $K^-_4$ -factor in a graph, J. Graph. Theory, 39 (2002), pp. 111-128, doi:10.1002/jgt.10007. · <a href="/0992.05059" class="nowrap">Zbl 0992.05059</a></td> </tr><tr> <td>[32]</td> <td class="space">Keevash, P., Knox, F., and Mycroft, R., Polynomial-time perfect matchings in dense hypergraphs, Adv. Math., 269 (2015), pp. 265-334, doi:10.1016/j.aim.2014.10.009. · <a href="/1303.05155" class="nowrap">Zbl 1303.05155</a></td> </tr><tr> <td>[33]</td> <td class="space">Kim, J., Kühn, D., Kupavskii, A., and Osthus, D., Rainbow structures in locally bounded colorings of graphs, Random Structures Algorithms, 56 (2020), pp. 1171-1204. · <a href="/1450.05070" class="nowrap">Zbl 1450.05070</a></td> </tr><tr> <td>[34]</td> <td class="space">Komlós, J., Tiling Turán theorems, Combinatorica, 20 (2000), pp. 203-218, doi:10.1007/s004930070020. · <a href="/0949.05063" class="nowrap">Zbl 0949.05063</a></td> </tr><tr> <td>[35]</td> <td class="space">Komlós, J., Sárközy, G., and Szemerédi, E., Proof of the Alon-Yuster conjecture, Discrete Math., 235 (2001), pp. 255-269. · <a href="/0977.05106" class="nowrap">Zbl 0977.05106</a></td> </tr><tr> <td>[36]</td> <td class="space">Komlós, J., Sárközy, G. N., and Szemerédi, E., Blow-up lemma, Combinatorica, 17 (1997), pp. 109-123. · <a href="/0880.05049" class="nowrap">Zbl 0880.05049</a></td> </tr><tr> <td>[37]</td> <td class="space">Komlós, J. and Simonovits, M., Szemerédi’s Regularity Lemma and its applications in graph theory, in Combinatorics Paul Erdős is Eighty, Vol. 2, (Keszthely, 1993), , János Bolyai Math. Soc., Budapest, 1996, pp. 295-352. · <a href="/0851.05065" class="nowrap">Zbl 0851.05065</a></td> </tr><tr> <td>[38]</td> <td class="space">Kotzig, A., Moves without forbidden transitions in a graph, Mat. Časopis Sloven. Akad. Vied, 18 (1968), pp. 76-80. · <a href="/0155.31901" class="nowrap">Zbl 0155.31901</a></td> </tr><tr> <td>[39]</td> <td class="space">Krivelevich, M., The critical bias for the Hamiltonicity game is $(1+o(1))n/\ln n$, J. Amer. Math. Soc., 24 (2011), pp. 125-131. · <a href="/1205.91042" class="nowrap">Zbl 1205.91042</a></td> </tr><tr> <td>[40]</td> <td class="space">Krivelevich, M., Lee, C., and Sudakov, B., Resilient pancyclicity of random and pseudorandom graphs, SIAM J. Discrete Math., 24 (2010), pp. 1-16, doi:10.1137/090761148. · <a href="/1215.05165" class="nowrap">Zbl 1215.05165</a></td> </tr><tr> <td>[41]</td> <td class="space">Krivelevich, M., Lee, C., and Sudakov, B., Robust Hamiltonicity of Dirac graphs, Trans. Amer. Math. Soc., 366 (2014), pp. 3095-3130. · <a href="/1290.05098" class="nowrap">Zbl 1290.05098</a></td> </tr><tr> <td>[42]</td> <td class="space">Krivelevich, M., Lee, C., and Sudakov, B., Compatible Hamilton cycles in random graphs, Random Structures Algorithms, 49 (2016), pp. 533-557. · <a href="/1349.05199" class="nowrap">Zbl 1349.05199</a></td> </tr><tr> <td>[43]</td> <td class="space">Krivelevich, M., Lee, C., and Sudakov, B., Compatible Hamilton cycles in Dirac graphs, Combinatorica, 37 (2017), pp. 697-732. · <a href="/1399.05143" class="nowrap">Zbl 1399.05143</a></td> </tr><tr> <td>[44]</td> <td class="space">Krivelevich, M. and Szabó, T., Biased positional games and small hypergraphs with large covers, Electron. J. Combin.15 (2008), R70. · <a href="/1160.91007" class="nowrap">Zbl 1160.91007</a></td> </tr><tr> <td>[45]</td> <td class="space">Kühn, D. and Osthus, D., The minimum degree threshold for perfect graph packings, Combinatorica, 29 (2009), pp. 65-107. · <a href="/1517.05143" class="nowrap">Zbl 1517.05143</a></td> </tr><tr> <td>[46]</td> <td class="space">Kühn, D., Osthus, D., and Treglown, A., An Ore-type theorem for perfect packings in graphs, SIAM J. Discrete Math., 23 (2009), pp. 1335-1355, doi:10.1137/080731256. · <a href="/1207.05059" class="nowrap">Zbl 1207.05059</a></td> </tr><tr> <td>[47]</td> <td class="space">Lo, A., Properly coloured Hamiltonian cycles in edge-coloured complete graphs, Combinatorica, 36 (2016), pp. 471-492. · <a href="/1389.05043" class="nowrap">Zbl 1389.05043</a></td> </tr><tr> <td>[48]</td> <td class="space">Lo, A. and Markström, K., F-factors in hypergraphs via absorption, Graphs Combin., 31 (2015), pp. 679-712. · <a href="/1312.05099" class="nowrap">Zbl 1312.05099</a></td> </tr><tr> <td>[49]</td> <td class="space">Montgomery, R., Spanning trees in random graphs, Adv. Math., 356 (2019), 106793. · <a href="/1421.05080" class="nowrap">Zbl 1421.05080</a></td> </tr><tr> <td>[50]</td> <td class="space">Montgomery, R., Pokrovskiy, A., and Sudakov, B., Embedding rainbow trees with applications to graph labelling and decomposition, J. Eur. Math. Soc., 22 (2020), pp. 3101-3132. · <a href="/1508.05024" class="nowrap">Zbl 1508.05024</a></td> </tr><tr> <td>[51]</td> <td class="space">Nenadov, R. and Pehova, Y., On a Ramsey-Turán variant of the Hajnal-Szemerédi theorem, SIAM J. Discrete Math., 34 (2020), pp. 1001-1010, doi:10.1137/18M1211970. · <a href="/1436.05087" class="nowrap">Zbl 1436.05087</a></td> </tr><tr> <td>[52]</td> <td class="space">Rödl, V., Ruciński, A., and Szemerédi, E., Perfect matchings in large uniform hypergraphs with large minimum collective degree, J. Combin. Theory Ser. A, 116 (2009), pp. 613-636. · <a href="/1214.05130" class="nowrap">Zbl 1214.05130</a></td> </tr><tr> <td>[53]</td> <td class="space">Shearer, J., A property of the colored complete graph, Discrete Math., 25 (1979), pp. 175-178. · <a href="/0397.05024" class="nowrap">Zbl 0397.05024</a></td> </tr><tr> <td>[54]</td> <td class="space">Shokoufandeh, A. and Zhao, Y., Proof of a tiling conjecture of Komlós, Random Structures Algorithms, 23 (2003), pp. 180-205, doi:10.1002/rsa.10091. · <a href="/1029.05121" class="nowrap">Zbl 1029.05121</a></td> </tr><tr> <td>[55]</td> <td class="space">Sudakov, B., Robustness of graph properties, in Surveys in Combinatorics 2017, , Cambridge University Press, Cambridge, 2017, pp. 372-408. · <a href="/1423.05186" class="nowrap">Zbl 1423.05186</a></td> </tr><tr> <td>[56]</td> <td class="space">Sudakov, B. and Vu, V. H., Local resilience of graphs, Random Structures Algorithms, 33 (2008), pp. 409-433. · <a href="/1182.05114" class="nowrap">Zbl 1182.05114</a></td> </tr><tr> <td>[57]</td> <td class="space">Yuster, R., Rainbow H-factors, Electron. J. Combin., 13 (2006), R13. · <a href="/1081.05095" class="nowrap">Zbl 1081.05095</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1521.05159 - zbMATH Open