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DOI: 10.4230/LIPIcs.IPEC.2019.21

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

Authors: Edin Husić, Stéphan Thomassé, and Nicolas Trotignon

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

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.

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Edin Husić, Stéphan Thomassé, and Nicolas Trotignon. The Independent Set Problem Is FPT for Even-Hole-Free Graphs. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{husic_et_al:LIPIcs.IPEC.2019.21,
  author =	{Husi\'{c}, Edin and Thomass\'{e}, St\'{e}phan and Trotignon, Nicolas},
  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 =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.21},
  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}
}

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

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