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.IPEC.2019.21
URN: urn:nbn:de:0030-drops-114826
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11482/
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Husic, Edin ; Thomassé, Stéphan ; Trotignon, Nicolas

The Independent Set Problem Is FPT for Even-Hole-Free Graphs

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LIPIcs-IPEC-2019-21.pdf (0.6 MB)

Abstract

The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem. However, the complexity of computing a maximum independent set (MIS) is a long-standing open question in even-hole-free graphs. From the hardness point of view, MIS is W[1]-hard in the class of graphs without induced 4-cycle (when parameterized by the solution size). Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs. The main idea is to apply twice the well-known technique of augmenting graphs to extend some initial independent set.

BibTeX - Entry

@InProceedings{husic_et_al:LIPIcs:2019:11482,
  author =	{Edin Husic and St{\'e}phan Thomass{\'e} and Nicolas Trotignon},
  title =	{{The Independent Set Problem Is FPT for Even-Hole-Free Graphs}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Bart M. P. Jansen and Jan Arne Telle},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11482},
  URN =		{urn:nbn:de:0030-drops-114826},
  doi =		{10.4230/LIPIcs.IPEC.2019.21},
  annote =	{Keywords: independent set, FPT algorithm, even-hole-free graph, augmenting graph}
}

Keywords: independent set, FPT algorithm, even-hole-free graph, augmenting graph
Collection: 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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