Document Zbl 1426.05138

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Math.</a> <a href="/?q=in%3A442099" title="Articles in this Issue">270, 181-189 (2019)</a>. </div> <div class="abstract">Summary: The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, <span class="zbmathjax-textit">Y. Liu</span> and <span class="zbmathjax-textit">W. Liu</span> [J. Comb. Optim. 34, No. 2, 522–533 (2017; <a href="/1376.05123">Zbl 1376.05123</a>)] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of $G$ is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of $G$ is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the FMP number and the FSMP number for arrangement graphs. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7127281">Cited in <strong>11</strong> Documents</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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amatching">matching</a>; <a href="/?q=ut%3Afractional+matching+preclusion">fractional matching preclusion</a>; <a href="/?q=ut%3Afractional+strong+matching+preclusion">fractional strong matching preclusion</a>; <a href="/?q=ut%3Aarrangement+graph">arrangement graph</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1376.05123">Zbl 1376.05123</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 1426.05138" data-ciurl="/ci/07127281" data-biburl="/bibtex/07127281.bib" data-amsurl="/amsrefs/07127281.bib" data-xmlurl="/xml/07127281.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07127281.pdf" title="Zbl 1426.05138 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/10.1016/j.dam.2019.07.014" aria-label="DOI for “Fractional matching preclusion for arrangement graphs”" title="10.1016/j.dam.2019.07.014">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Akers, S. B.; Harel, D.; Krishnamurthy, B., The star graph: an attractive alternative to the $n$-cube, (Proc. Int. Conf. Parallel Processing, ICPP’1987 (1987), University Park), 393-400</td> </tr><tr> <td>[2]</td> <td class="space">Bondy, J. A.; Murty, U. S.R., Graph theory, (GTM 244 (2008), Springer) · <a href="/1134.05001" class="nowrap">Zbl 1134.05001</a></td> </tr><tr> <td>[3]</td> <td class="space">Bonneville, P.; Cheng, E.; Renzi, J., Strong matching preclusion for the alternating group graphs and split stars, JOIN, 12, 277-298 (2011)</td> </tr><tr> <td>[4]</td> <td class="space">Brigham, R. C.; Harary, F.; Violin, E. C.; Yellen, J., Perfect-matching preclusion, Congr. Numer., 174, 185-192 (2005) · <a href="/1091.05057" class="nowrap">Zbl 1091.05057</a></td> </tr><tr> <td>[5]</td> <td class="space">Chang, W.; Cheng, E., Strong matching preclusion of $2$-matching composition networks, Congr. 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H., Fractional Graph Theory: A Rational Approach to the Theory of Graphs (1997), John Wiley: John Wiley New York · <a href="/0891.05003" class="nowrap">Zbl 0891.05003</a></td> </tr><tr> <td>[22]</td> <td class="space">Tutte, W. T., The factorization of linear graphs, J. Lond. Math. Soc., 22, 107-111 (1947) · <a href="/0029.23301" class="nowrap">Zbl 0029.23301</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>

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