Document Zbl 0859.05001

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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/diestel.reinhard" title="Author Profile">Diestel, Reinhard</a></div> <h2 class="title"> <strong>Graph theory. (Graphentheorie.)</strong> <i>(German)</i> <a class="label nowrap" href="/0859.05001">Zbl 0859.05001</a> </h2> <div class="source"> Berlin: Springer. xiv, 290 p. (1996). </div> <div class="abstract">The flavor of this textbook is perhaps best conveyed by listing the chapters and their sections. 0. Fundamentals: Graphs. The degree of a vertex. Paths and cycles. Connectivity. Trees and forests. Bipartite graphs. Contraction and minors. Eulerian graphs. Algebraic concepts. Related concepts. 1. Matchings: Matchings in bipartite graphs. Matchings in general graphs. Coverings by disjoint paths. 2. Connectivity: 2-connected graphs and subgraphs. The structure of 3-connected graphs. The theorem of Menger. The theorem of Mader. Edge-disjoint spanning trees. Linking paths with given end vertices. 3. Graphs in the Plane: Topological prerequisites. Plane graphs. Drawings. Planarity: Kuratowski’s theorem. Algebraic planarity criteria. Planarity and duality. 4. Colorings: Maps and colors of plane graphs. Vertex colorings. Edge colorings. List colorings. Perfect graphs. 5. Flows: Flows. Flows and circulations. Networks. $k$-flows for small $k$. Flows and colorings. Tutte’s flow conjectures. 6. Substructures: Subgraphs. Topological minors. Minors. The Hadwiger conjecture. The regularity lemma. 7. Ramsey Theory for Graphs: Ramsey’s theorem. Ramsey numbers of graphs. Ramsey induced. Ramsey theorems and connectivity. 8. Hamiltonian Cycles: Simple sufficient conditions. Hamiltonian cycles and degree sequence. Hamiltonian cycles in the square of a graph. 9. Random Graphs: The concept of random graphs. The probabilistic method. Properties of almost all graphs. Threshold functions and second moments. 10. Minors, Trees, and the WQO: Well-quasi-ordering. Trees: Kruskal’s theorem. Tree decompositions. The theorem on minors.<br class="zbmathjax-paragraph">A few results are included without proofs but, for the most part, clean, concise arguments are provided. The exercises, 250 in all, are collected at the end of each chapter. These are followed by notes concomitant with the text, e.g., they include sources for many of the proofs, further references, and historical remarks. Problems are an essential part of any textbook and the selection here is appropriate. Some exercises are graded for difficulty. Some state results that follow directly from theorems but are required to be proved ab initio.<br class="zbmathjax-paragraph">Several distinguishing features contribute to the comfortable ‘feel’ of this book. For example, symbols and terms being defined are listed in the margin; these margins also contain extensive cross referencing. The index contains the English equivalents for technical terms. In addition, the author includes a brief English to German dictionary of technical terminology. In the Forward he gives a web site address to which readers may send errors or misprints; it contained no entries at the time of this writing.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A432">R.C.Entringer (Albuquerque)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A945671">Cited in <strong>8</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A945671">Cited in <strong>17</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05-01" title="MSC2020">05-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05Cxx" title="MSC2020">05Cxx</a> </td> <td class="space"> Graph theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apaths">paths</a>; <a href="/?q=ut%3Aconnectivity">connectivity</a>; <a href="/?q=ut%3Atrees">trees</a>; <a href="/?q=ut%3Amatchings">matchings</a>; <a href="/?q=ut%3Acoverings">coverings</a>; <a href="/?q=ut%3Aperfect+graphs">perfect graphs</a>; <a href="/?q=ut%3Awell-quasi-ordering">well-quasi-ordering</a>; <a href="/?q=ut%3Atextbook">textbook</a>; <a href="/?q=ut%3Acycles">cycles</a>; <a href="/?q=ut%3AEulerian+graphs">Eulerian graphs</a>; <a href="/?q=ut%3Abipartite+graphs">bipartite graphs</a>; <a href="/?q=ut%3Atheorem+of+Menger">theorem of Menger</a>; <a href="/?q=ut%3Atheorem+of+Mader">theorem of Mader</a>; <a href="/?q=ut%3Aspanning+trees">spanning trees</a>; <a href="/?q=ut%3AKuratowski%27s+theorem">Kuratowski’s theorem</a>; <a href="/?q=ut%3Aplanarity">planarity</a>; <a href="/?q=ut%3Acolors">colors</a>; <a href="/?q=ut%3Aplane+graphs">plane graphs</a>; <a href="/?q=ut%3Acolorings">colorings</a>; <a href="/?q=ut%3ATutte%27s+flow+conjectures">Tutte’s flow conjectures</a>; <a href="/?q=ut%3Aminors">minors</a>; <a href="/?q=ut%3AHadwiger+conjecture">Hadwiger conjecture</a>; <a href="/?q=ut%3Aregularity+lemma">regularity lemma</a>; <a href="/?q=ut%3ARamsey%27s+theorem">Ramsey’s theorem</a>; <a href="/?q=ut%3ARamsey+numbers">Ramsey numbers</a>; <a href="/?q=ut%3AHamiltonian+cycles">Hamiltonian cycles</a>; <a href="/?q=ut%3Arandom+graphs">random graphs</a>; <a href="/?q=ut%3Aprobabilistic+method">probabilistic method</a>; <a href="/?q=ut%3AKruskal%27s+theorem">Kruskal’s theorem</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 0859.05001" data-ciurl="/ci/00945671" data-biburl="/bibtex/00945671.bib" data-amsurl="/amsrefs/00945671.bib" data-xmlurl="/xml/00945671.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00945671.pdf" title="Zbl 0859.05001 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="http://www.emis.de///monographs/Diestel/de/" title="Open Access at EMIS">EMIS</a> </div> <div class="sfx" style="float: right;"> </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 = ""; 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