An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8" /> <title>An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius</title>  <link rel="shortcut icon" type="image/ico" href="./data/toc/coversheet/favicon.ico" />  <meta name="viewport" content="width=device-width, maximum-scale=1, initial-scale=1, user-scalable=0" />   <meta name="keywords" content="$k$-uniform $k$-partite hypergraphs,Distance spectral radius,perfect matching" /> <meta name="description" content="Let $n_1, n_2,\ldots,n_k$ be integers and $V_1, V_2,\ldots,V_k$ be disjoint vertex sets with $|V_i|=n_i$ for each $i= 1, 2,\ldots,k$. A $k$-partite $k$-uniform hypergraph on vertex classes $V_1, V_2,\ldots,V_k$ is defined to be the $k$-uniform hypergraph whose edge set consists of the $k$-element subsets $S$ of $V_1 \cup V_2 \cup \cdots \cup V_k$ such that $|S\cap V_i|=1$ for all $i= 1, 2,\ldots,k$. We say that it is balanced if $n_1=n_2=\cdots=n_k$. In this paper, we give a distance spectral radius condition to guarantee the existence of perfect matching in $k$-partite $k$-uniform hypergraphs, this result generalize the result of Zhang and Lin 聽[Perfect matching and distance spectral radius in graphs and bipartite graphs, Discrete Appl. Math., 304 (2021) 315-322]." /> <meta name="title" content="An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius" /> <meta name="googlebot" content="NOODP" /> <meta name="citation_title" content="An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius" /> <meta name="citation_author" content="Zhang, Lei" /> <meta name="citation_author_institution" content="Department of Mathematics and Statistics, Qinghai Normal University, Xining, China" /> <meta name="citation_author" content="Ren, Haizhen" /> <meta name="citation_author_institution" content="Department of Mathematics and Statistics, Qinghai Normal University, Xining, China" /> <meta name="citation_abstract" content="Let $n_1, n_2,\ldots,n_k$ be integers and $V_1, V_2,\ldots,V_k$ be disjoint vertex sets with $|V_i|=n_i$ for each $i= 1, 2,\ldots,k$. A $k$-partite $k$-uniform hypergraph on vertex classes $V_1, V_2,\ldots,V_k$ is defined to be the $k$-uniform hypergraph whose edge set consists of the $k$-element subsets $S$ of $V_1 \cup V_2 \cup \cdots \cup V_k$ such that $|S\cap V_i|=1$ for all $i= 1, 2,\ldots,k$. We say that it is balanced if $n_1=n_2=\cdots=n_k$. In this paper, we give a distance spectral radius condition to guarantee the existence of perfect matching in $k$-partite $k$-uniform hypergraphs, this result generalize the result of Zhang and Lin 聽[Perfect matching and distance spectral radius in graphs and bipartite graphs, Discrete Appl. Math., 304 (2021) 315-322]." /> <meta name="citation_id" content="27945" /> <meta name="citation_publication_date" content="2024/12/01" /> <meta name="citation_date" content="2024-12-01" /> <meta name="citation_journal_title" content="Transactions on Combinatorics" /> <meta name="citation_issn" content="2251-8657" /> <meta name="citation_volume" content="13" /> <meta name="citation_issue" content="4" /> <meta name="citation_firstpage" content="377" /> <meta name="citation_lastpage" content="385" /> <meta name="citation_publisher" content="University of Isfahan" /> <meta name="citation_doi" content="10.22108/toc.2023.137937.2077" /> <meta name="DC.Identifier" content="10.22108/toc.2023.137937.2077" /> <meta name="citation_abstract_html_url" content="https://toc.ui.ac.ir/article_27945.html" /> <meta name="citation_pdf_url" content="https://toc.ui.ac.ir/article_27945_1541186ba65820112fd9979a333aaf05.pdf" /> <meta name="DC.Title" content="An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius" /> <meta name="DC.Source" content="Transactions on Combinatorics" /> <meta name="DC.Date" content="01/12/2024" /> <meta name="DC.Date.issued" content="2024-12-01" /> <meta name="DC.Format" content="application/pdf" /> <meta name="DC.Contributor" content="Zhang, Lei" /> <meta name="DC.Contributor" content="Ren, Haizhen" /> <meta name="og:title" content="An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius" /> <meta name="og:description" content="Let $n_1, n_2,\ldots,n_k$ be integers and $V_1, V_2,\ldots,V_k$ be disjoint vertex sets with $|V_i|=n_i$ for each $i= 1, 2,\ldots,k$. A $k$-partite $k$-uniform hypergraph on vertex classes $V_1, V_2,\ldots,V_k$ is defined to be the $k$-uniform hypergraph whose edge set consists of the $k$-element subsets $S$ of $V_1 \cup V_2 \cup \cdots \cup V_k$ such that $|S\cap V_i|=1$ for all $i= 1, 2,\ldots,k$. We say that it is balanced if $n_1=n_2=\cdots=n_k$. In this paper, we give a distance spectral radius condition to guarantee the existence of perfect matching in $k$-partite $k$-uniform hypergraphs, this result generalize the result of Zhang and Lin 聽[Perfect matching and distance spectral radius in graphs and bipartite graphs, Discrete Appl. Math., 304 (2021) 315-322]." /> <meta name="og:url" content="https://toc.ui.ac.ir/article_27945.html" />   <link href="./themes/base/front/assets/plugins/bootstrap/css/bootstrap.min.css?v=0.02" rel="stylesheet" type="text/css" /> <link href="./inc/css/ju_css.css" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/header.css?v=0.015" rel="stylesheet" type="text/css" />  <link href="./themes/base/front/assets/plugins/bootstrap/css/bootstrap-ltr.min.css" rel="stylesheet" type="text/css" /> <link href=" ./themes/base/front/assets/css/gfonts-Arial.css" rel="stylesheet" type="text/css" />  <link href="./data/toc/coversheet/stl_front.css?v=0.12" rel="stylesheet" type="text/css" />  <link rel="alternate" type="application/rss+xml" title="RSS feed" href="./ju.rss" /> <script type="text/javascript" src="./inc/js/app.js?v=0.1"></script>   <script type="text/javascript">MathJax = {tex: {inlineMath: [['$', '$'], ['\$','\$']]}};</script> <script type="text/javascript" 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href="./?_action=article&au=274075&_au=Lei++Zhang">Lei Zhang</a> <sup class="ltr"><a class=" text-green" href="https://orcid.org/0000-0001-5187-7898" data-toggle="tooltip" data-placement="bottom" data-html="true" title="ORCID: 0000-0001-5187-7898" target="_blank"><i class="ai ai-orcid size-13" ></i></a></sup> </li> <li class="padding-3"> <a href="./?_action=article&au=274076&_au=Haizhen++Ren">Haizhen Ren</a> <sup><a href="mailto:haizhenr@126.com" data-toggle="tooltip" data-placement="bottom" title="Email to Corresponding Author"><i class="fa fa-envelope-o" ></i></a></sup> <sup class="ltr"><a class=" text-green" href="https://orcid.org/0000-0001-5609-5924" data-toggle="tooltip" data-placement="bottom" data-html="true" title="ORCID: 0000-0001-5609-5924" target="_blank"><i class="ai ai-orcid size-13" ></i></a></sup> </li> </ul> <p class="margin-bottom-3 ltr" id="aff1"> Department of Mathematics and Statistics, Qinghai Normal University, Xining, China </p> <div class="margin-bottom-3 ltr" id="ar_doi" title="DOI"><i class="ai ai-doi size-25 text-orange"></i> <span dir="ltr"><a href="https://doi.org/10.22108/toc.2023.137937.2077">10.22108/toc.2023.137937.2077</a></span></div> <p style="margin:12px -2px 0 -2px"><strong>Abstract</strong></p> <div class="padding_abstract justify ltr">Let $n_1, n_2,\ldots,n_k$ be integers and $V_1, V_2,\ldots,V_k$ be disjoint vertex sets with $|V_i|=n_i$ for each $i= 1, 2,\ldots,k$. A $k$-partite $k$-uniform hypergraph on vertex classes $V_1, V_2,\ldots,V_k$ is defined to be the $k$-uniform hypergraph whose edge set consists of the $k$-element subsets $S$ of $V_1 \cup V_2 \cup \cdots \cup V_k$ such that $|S\cap V_i|=1$ for all $i= 1, 2,\ldots,k$. We say that it is balanced if $n_1=n_2=\cdots=n_k$. In this paper, we give a distance spectral radius condition to guarantee the existence of perfect matching in $k$-partite $k$-uniform hypergraphs, this result generalize the result of Zhang and Lin  [Perfect matching and distance spectral radius in graphs and bipartite graphs, <em>Discrete Appl. Math.,</em> <strong>304 </strong>(2021) 315-322].</div> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Keywords</strong></p> <ul class="block list-inline list-inline-seprator margin-bottom-6 ltr"> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=136223&_kw=%24k%24-uniform+%24k%24-partite+hypergraphs" >$k$-uniform $k$-partite hypergraphs</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=136224&_kw=Distance+spectral+radius" >Distance spectral radius</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=110352&_kw=Perfect+matching" >Perfect matching</a> </li> </ul> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Main Subjects</strong></p> <ul class="block list-inline list-inline-seprator margin-bottom-6"> <li class="padding-3"> <a href="./?_action=article&sb=352&_sb=05C+Combinatorics%3A+Graph+theory" >05C Combinatorics: Graph theory</a> </li> </ul> </div> <hr> <div class="page_break"></div> <div class="panel"> <div class="panel-heading card-header"> <h4 class="panel-title "> <a data-toggle="collapse" data-parent="#accordions" href="#collapsesRef"><i class="fa fa-plus"></i> References</a> </h4> </div> <div id="collapsesRef" class="panel-collapse collapse"> <div class="panel-body justify"> <div class="padding-3 margin-top-3 ltr justify">[1] M. Aouchiche and P. Hansen, Distance spectra of graphs: A survey, Linear Algebra Appl., 458 (2014) 301–386.<br />[2] C. Berge, Hypergraph: Combinatorics of Finite Sets, Elsevier, North-Holland, 1973.<br />[3] A. Bretto, Hypergraph Theory: An Introduction, Springer, Berlin, 2013.<br />[4] A. Brouwer, W. Haemers, Spectra of Graphs, Springer, Berlin, 2011.<br />[5] J. Edmonds, Path, trees and flowers, Canadian J. Math., 17 (1965) 449–467.<br />[6] J. Golzari, A generalization of Hall’s theorem for k-uniform k-partite hypergraphs, Trans. Comb., 8 (2019) 23–28.<br />[7] R. L. Graham and H. O. Pollack, On the addressing problem for loop switching, Bell Syst. Tech. J., 50 (1971) 2495–2519.<br />[8] H. Ha虁n, Y. Person and M. Schacht, On perfect matchings in uniform hypergraphs with large minimum vertex degree, SIAM J. Discrete Math. , 23 (2009) 732–748.<br />[9] L. Hogben and C. Reinhart, Spectra of variants of distance matrices of graphs and digraphs: a survey, La Matematica., 1 (2022) 186–224. </div> <div class="padding-3 margin-top-3 ltr justify">[10] R. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations, Springer, Berlin, 1972.<br />[11] H. Lin, J. Shu, J. Xue and Y. Zhang, A survey on distance spectra of graphs, Adv. Math., 50 (2021) 29–76.<br />[12] H. Lin and Y. Zhang, Extremal problems on distance spectra of graphs, Discrete Appl. Math., 289 (2021) 139–147.<br />[13] H. Lin and B. Zhou, Distance spectral radius of uniform hypergraphs, Linear Algebra Appl., 506 (2016) 564–578.<br />[14] H. Lin and B. Zhou, On distance spectral radius of uniform hypergraphs with cycles, Discrete Appl. Math., 239 (2018) 125–143.<br />[15] H. Lin, B. Zhou and Y. Wang, Distance (signless) Laplacian spectral radius of uniform hypergraphs, Linear Algebra Appl., 529 (2017) 271–293.<br />[16] Z. Lou and H. Lin, Distance eigenvalues of a cograph and their multiplicities, Linear Algebra Appl., 608 (2021) 1–12.<br />[17] J. Rodriguez, On the Wiener index and the eccentric distance sum of hypergraphs, Math. Commun. Math. Comput. Chem. 54 (2005) 209-220.<br />[18] V. Ro虉dl, A. Rucin虂ski and E. Szemere虂di, Perfect matchings in large uniform hypergraphs with large minimum collective degree, J. Combin. Theory Ser. A, 116 (2009) 616–636.<br />[19] S. Sivasubramanian, q-analogs of distance matrices of 3-hypertrees, Linear Algebra Appl., 431 (2009) 1234–1248.<br />[20] A. Treglown and Y. Zhao, Exact minimum degree thresholds for perfect matchings in uniform hypergraphs, J. Combin. Theory Ser. A, 119 (2012) 1500–1522.<br />[21] Y. Wang and B. Zhou, On distance spectral radius of hypergraphs, Linear Multilinear A, 66 (2018) 2232–2246.<br />[22] Y. Zhang and H. Lin, Perfect matching and distance spectral radius in graphs and bipartite graphs, Discrete Appl. Math., 304 (2021) 315–322.</div> </div> </div> </div> </div> </div>   <div class="col-lg-3 col-md-3 col-sm-4"> <div class="panel panel-default my_panel-default margin-bottom-10"> <div class="panel-body ar_info_pnl" id="ar_info_pnl_cover"> <div id="pnl_cover"> <div class="row" > <div class="col-xs-6 col-md-6 nomargin-bottom"> <a href="javascript:loadModal('Transactions on Combinatorics', './data/toc/coversheet/cover_en.jpg')"> <img src="data/toc/coversheet/cover_en.jpg" alt="Transactions on Combinatorics" style="width: 100%;"> </a> </div> <div class="col-xs-6 col-md-6 nomargin-bottom"> <h6><a href="./issue_5051_5056.html">Volume 13, Issue 4 - Serial Number 4</a><br/>December 2024<div id="sp_ar_pages">Pages <span dir="ltr">377-385</span></div></h6> </div> </div> </div> </div> </div>  <div class="panel panel-default my_panel-default margin-bottom-10 panel-lists"> <div class="panel-heading"> <h3 class="panel-title"><a data-toggle="collapse" data-parent="#accordion" 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id="ar_info_pnl_st" class="panel-collapse collapse in"> <div class="panel-body ar_info_pnl"> <ul class="list-group list-group-bordered list-group-noicon" style="display:block !important;max-height:9999px"> <li class="list-group-item"><a class="tag_a">Article View: <i>272</i></a></li> <li class="list-group-item"><a class="tag_a">PDF Download: <i>572</i></a></li> </ul> </div> </div> </div> </div>  </div> </section> <div id="cite-apa" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">APA</h4> </div>  <div class="modal-body"> <p> Zhang, L. and Ren, H. (2024). An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius. <em>Transactions on Combinatorics</em>, <em>13</em>(4), 377-385. doi: 10.22108/toc.2023.137937.2077</p> </div> </div> </div> </div> <div id="cite-mla" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">MLA</h4> </div>  <div class="modal-body"> <p> Zhang, L. , and Ren, H. . "An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius", <em>Transactions on Combinatorics</em>, 13, 4, 2024, 377-385. doi: 10.22108/toc.2023.137937.2077</p> </div> </div> </div> </div> <div id="cite-harvard" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">HARVARD</h4> </div>  <div class="modal-body"> <p>Zhang, L., Ren, H. (2024). 'An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius', <em>Transactions on Combinatorics</em>, 13(4), pp. 377-385. doi: 10.22108/toc.2023.137937.2077</p> </div> </div> </div> </div> <div id="cite-chicago" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">CHICAGO</h4> </div>  <div class="modal-body"> <p> L. Zhang and H. Ren, "An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius," Transactions on Combinatorics, 13 4 (2024): 377-385, doi: 10.22108/toc.2023.137937.2077</p> </div> </div> </div> </div> <div id="cite-vancouver" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">VANCOUVER</h4> </div>  <div class="modal-body"> <p>Zhang, L., Ren, H. An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius. <em>Transactions on Combinatorics</em>, 2024; 13(4): 377-385. doi: 10.22108/toc.2023.137937.2077</p> </div> </div> </div> </div> </div> </div>   <section class="alternate padding-xxs"> </section>   <div class="container"> <footer id="footer"> <div class="scrollup" id="scroll" href="#"><span></span></div> <div class="row"> <div class="col-md-2">  <h4 class="">Explore Journal</h4> <ul class="footer-links list-unstyled"> <li id="fli_home"><a href="./">Home</a></li> <li id="fli_about"><a href="./journal/about">About Journal</a></li> <li id="fli_Edb"><a href="./journal/editorial.board">Editorial Board</a></li> <li id="fli_submit"><a href="./author">Submit Manuscript</a></li> <li id="fli_contactus"><a href="./journal/contact.us">Contact Us</a></li> <li id="fli_sitemap"><a href="./sitemap.xml?usr">Sitemap</a></li> </ul>  </div> <div class="col-md-3">  <h4 class="">Latest News</h4> <ul class="footer-posts list-unstyled"> <li> <a href="./news?newsCode=317">TOC is accepted for inclusion in SCOPUS</a> <small class="ltr">2018-09-24</small> </li> <li> <a href="./news?newsCode=233">TOC is indexed in Emerging Sources Citation Index (an index in the Web of Science™ Core Collection)</a> <small class="ltr">2015-12-15</small> </li> <li> <a href="./news?newsCode=12">TOC received the credit of ELMI-PAJOHESHI</a> <small class="ltr">2012-01-26</small> </li> <li> <a href="./news?newsCode=10">Style File of TOC (new)</a> <small class="ltr">2012-01-25</small> </li> </ul>  </div> <div class="col-md-3">  <div><p style="line-height: 1.5;" align="center"><strong>Transactions on Combinatorics</strong></p> <p style="line-height: 1.5;" align="center"> </p> <p style="line-height: 1.5;" align="center"><img src="data/toc/news/88x31.png" alt="" width="147" height="52" /></p> <p style="text-align: center;"> </p></div>  </div> <div class="col-md-4">  <h4 class="">Newsletter Subscription</h4> <p>Subscribe to the journal newsletter and receive the latest news and updates</p> <form class="validate" action="" method="post" data-success="Subscription saved successfully." data-toastr-position="bottom-right"> <input type="hidden" name="_token" value="538002913baaba627a2e5df77f04b5719dd5532ab097b276"/> <div class="input-group"> <span class="input-group-addon"><i class="fa fa-envelope"></i></span> <input type="email" id="email" name="email" required="required" class="form-control required sbs_email" placeholder="Enter your Email" oninvalid="this.setCustomValidity('Enter a valid email address.')" oninput="this.setCustomValidity('')"> <span class="input-group-btn"> <button class="btn btn-primary mybtn" type="submit">Subscribe</button> </span> </div> </form>   <div class="margin-top-20"> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Facebook"> <i class="fa fa-facebook-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Twitter"> <i class="fa fa-twitter-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Linkedin"> <i class="fa fa-linkedin-square" aria-hidden="true"></i> </a> <a class="noborder" href="./ju.rss" class="social-icon social-icon-border social-rss pull-left block" data-toggle="tooltip" data-placement="top" title="Rss"><i class="fa fa-rss-square" aria-hidden="true"></i></a> </div> </div> </div> <div class="copyright" style="position: relative"> <ul class="nomargin list-inline mobile-block"> <li>© Journal management system. <span id='sp_crt'>designed by <a target='_blank' href='https://www.sinaweb.net/'>sinaweb</a></span></li> </ul> </div> </footer> </div>  </div>   <a href="#" id="toTop_old"></a>  <div id="preloader"> <div class="inner"> <span class="loader"></span> </div> </div>    <script type="text/javascript"> $('ul.nav li.dropdown').hover(function() { if (window.matchMedia('(max-width: 767px)').matches) return; 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An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius