License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2020.26
URN: urn:nbn:de:0030-drops-122731
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12273/
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Grüttemeier, Niels ; Komusiewicz, Christian ; Morawietz, Nils

Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs

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LIPIcs-SWAT-2020-26.pdf (0.6 MB)

Abstract

Given an undirected graph G and integers c and k, the Maximum Edge-Colorable Subgraph problem asks whether we can delete at most k edges in G to obtain a graph that has a proper edge coloring with at most c colors. We show that Maximum Edge-Colorable Subgraph admits, for every fixed c, a linear-size problem kernel when parameterized by the edge deletion distance of G to a graph with maximum degree c-1. This parameterization measures the distance to instances that, due to Vizing’s famous theorem, are trivial yes-instances. For c≤ 4, we also provide a linear-size kernel for the same parameterization for Multi Strong Triadic Closure, a related edge coloring problem with applications in social network analysis. We provide further results for Maximum Edge-Colorable Subgraph parameterized by the vertex deletion distance to graphs where every component has order at most c and for the list-colored versions of both problems.

BibTeX - Entry

@InProceedings{grttemeier_et_al:LIPIcs:2020:12273,
  author =	{Niels Gr{\"u}ttemeier and Christian Komusiewicz and Nils Morawietz},
  title =	{{Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Susanne Albers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12273},
  URN =		{urn:nbn:de:0030-drops-122731},
  doi =		{10.4230/LIPIcs.SWAT.2020.26},
  annote =	{Keywords: Graph coloring, social networks, parameterized complexity, kernelization}
}

Keywords: Graph coloring, social networks, parameterized complexity, kernelization
Collection: 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
Issue Date: 2020
Date of publication: 12.06.2020

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