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URN: urn:nbn:de:0030-drops-70042
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Independent Sets near the Lower Bound in Bounded Degree Graphs

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Abstract

By Brook's Theorem, every n-vertex graph of maximum degree at most Delta >= 3 and clique number at most Delta is Delta-colorable, and thus it has an independent set of size at least n/Delta. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an independent set of size at least n/Delta+k has a kernel of size O(k).

BibTeX - Entry

@InProceedings{dvork_et_al:LIPIcs:2017:7004,
  author =	{Zdenek Dvor{\'a}k and Bernard Lidick{\'y}},
  title =	{{Independent Sets near the Lower Bound in Bounded Degree Graphs}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte Vallée},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7004},
  URN =		{urn:nbn:de:0030-drops-70042},
  doi =		{10.4230/LIPIcs.STACS.2017.28},
  annote =	{Keywords: independent set, bounded degree, Delta-colorable, fixed parameter tractability}
}

Keywords: independent set, bounded degree, Delta-colorable, fixed parameter tractability
Seminar: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue date: 2017
Date of publication: 2017


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