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.STACS.2017.28
URN: urn:nbn:de:0030-drops-70042
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7004/
Dvorák, Zdenek ;
Lidický, Bernard
Independent Sets near the Lower Bound in Bounded Degree Graphs
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: |
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independent set, bounded degree, Delta-colorable, fixed parameter tractability |
Collection: |
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34th Symposium on Theoretical Aspects of Computer Science (STACS 2017) |
Issue Date: |
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2017 |
Date of publication: |
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06.03.2017 |