Document Zbl 07651181

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ESA 2020, September 7–9, 2020, Pisa, Italy, virtual conference. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 173, Article 42, 15 p. (2020). </div> <div class="abstract">Summary: The line graph of a graph $G$ is the graph $L(G)$ whose vertex set is the edge set of $G$ and there is an edge between $e,f\in E(G)$ if $e$ and $f$ share an endpoint in $G$. A graph is called line graph if it is a line graph of some graph. We study the Line-Graph-Edge Deletion problem, which asks whether we can delete at most $k$ edges from the input graph $G$ such that the resulting graph is a line graph. More precisely, we give a polynomial kernel for Line-Graph-Edge Deletion with $\mathcal{O}(k^5)$ vertices. This answers an open question posed by Falk Hüffner at Workshop on Kernels (WorKer) in 2013.<br class="zbmathjax-paragraph">For the entire collection see [<a href="/1445.68017">Zbl 1445.68017</a>].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7651181">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%3A68Wxx" title="MSC2020">68Wxx</a> </td> <td class="space"> Algorithms in computer science </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Akernelization">kernelization</a>; <a href="/?q=ut%3Aline+graphs">line graphs</a>; <a href="/?q=ut%3A%5C%28H%5C%29-free+editing">$H$-free editing</a>; <a href="/?q=ut%3Agraph+modification+problem">graph modification problem</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 07651181" data-ciurl="/ci/07651181" data-biburl="/bibtex/07651181.bib" data-amsurl="/amsrefs/07651181.bib" data-xmlurl="/xml/07651181.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07651181.pdf" title="Zbl 07651181 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/10.4230/LIPIcs.ESA.2020.42" aria-label="DOI for “A polynomial kernel for line graph deletion”" title="10.4230/LIPIcs.ESA.2020.42">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2006.15584"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">N. 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