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.2020.5
URN: urn:nbn:de:0030-drops-133087
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13308/
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Bożyk, Łukasz ; Derbisz, Jan ; Krawczyk, Tomasz ; Novotná, Jana ; Okrasa, Karolina

Vertex Deletion into Bipartite Permutation Graphs

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LIPIcs-IPEC-2020-5.pdf (0.8 MB)


Abstract

A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines 𝓁₁ and 𝓁₂, one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation vertex deletion problem, which asks, for a given n-vertex graph, whether we can remove at most k vertices to obtain a bipartite permutation graph. This problem is NP-complete by the classical result of Lewis and Yannakakis [John M. Lewis and Mihalis Yannakakis, 1980]. We analyze the structure of the so-called almost bipartite permutation graphs which may contain holes (large induced cycles) in contrast to bipartite permutation graphs. We exploit the structural properties of the shortest hole in a such graph. We use it to obtain an algorithm for the bipartite permutation vertex deletion problem with running time f(k)n^O(1), and also give a polynomial-time 9-approximation algorithm.

BibTeX - Entry

@InProceedings{boyk_et_al:LIPIcs:2020:13308,
  author =	{Łukasz Bożyk and Jan Derbisz and Tomasz Krawczyk and Jana Novotn{\'a} and Karolina Okrasa},
  title =	{{Vertex Deletion into Bipartite Permutation Graphs}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13308},
  URN =		{urn:nbn:de:0030-drops-133087},
  doi =		{10.4230/LIPIcs.IPEC.2020.5},
  annote =	{Keywords: permutation graphs, comparability graphs, partially ordered set, graph modification problems}
}

Keywords: permutation graphs, comparability graphs, partially ordered set, graph modification problems
Collection: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue Date: 2020
Date of publication: 04.12.2020


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