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.FSTTCS.2016.21
URN: urn:nbn:de:0030-drops-68561
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6856/
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Rai, Ashutosh ; Ramanujan, M. S.

Strong Parameterized Deletion: Bipartite Graphs

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LIPIcs-FSTTCS-2016-21.pdf (0.6 MB)

Abstract

The purpose of this article is two fold: (a) to formally introduce a stronger version of graph deletion problems; and (b) to study this version in the context of bipartite graphs. Given a family of graphs F, a typical instance of parameterized graph deletion problem consists of an undirected graph G and a positive integer k and the objective is to check whether we can delete at most k vertices (or k edges) such that the resulting graph belongs to F. Another version that has been recently studied is the one where the input contains two integers k and l and the objective is to check whether we can delete at most k vertices and l edges such that the resulting graph belongs to F. In this paper, we propose and initiate the study of a more general version which we call strong deletion. In this problem, given an undirected graph G and positive integers k and l, the objective is to check whether there exists a vertex subset S of size at most k such that each connected component of G-S can be transformed into a graph in F by deleting at most l edges. In this paper we study this stronger version of deletion problems for the class of bipartite graphs. In particular, we study Strong Bipartite Deletion, where given an undirected graph G and positive integers k and l, the objective is to check whether there exists a vertex subset S of size at most k such that each connected component of G-S can be made bipartite by deleting at most l edges. While fixed-parameter tractability when parameterizing by k or l alone is unlikely, we show that this problem is fixed-parameter tractable (FPT) when parameterized by both k and l.

BibTeX - Entry

@InProceedings{rai_et_al:LIPIcs:2016:6856,
  author =	{Ashutosh Rai and M. S. Ramanujan},
  title =	{{Strong Parameterized Deletion: Bipartite Graphs}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6856},
  URN =		{urn:nbn:de:0030-drops-68561},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.21},
  annote =	{Keywords: fixed parameter tractable, bipartite-editing, recursive understanding}
}

Keywords: fixed parameter tractable, bipartite-editing, recursive understanding
Collection: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)
Issue Date: 2016
Date of publication: 10.12.2016

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