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DOI: 10.4230/LIPIcs.IPEC.2015.270
URN: urn:nbn:de:0030-drops-55893
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5589/
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Kim, Eun Jung ; Kwon, O-joung

A Polynomial Kernel for Block Graph Deletion

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Abstract

In the Block Graph Deletion problem, we are given a graph G on n vertices and a positive integer k, and the objective is to check whether it is possible to delete at most k vertices from G to make it a block graph, i.e., a graph in which each block is a clique. In this paper, we obtain a kernel with O(k^{6}) vertices for the Block Graph Deletion problem. This is a first step to investigate polynomial kernels for deletion problems into non-trivial classes of graphs of bounded rank-width, but unbounded tree-width. Our result also implies that Chordal Vertex Deletion admits a polynomial-size kernel on diamond-free graphs. For the kernelization and its analysis, we introduce the notion of 'complete degree' of a vertex. We believe that the underlying idea can be potentially applied to other problems. We also prove that the Block Graph Deletion problem can be solved in time 10^{k} * n^{O(1)}.

BibTeX - Entry

@InProceedings{kim_et_al:LIPIcs:2015:5589,
  author =	{Eun Jung Kim and O-joung Kwon},
  title =	{{A Polynomial Kernel for Block Graph Deletion}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{270--281},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5589},
  URN =		{urn:nbn:de:0030-drops-55893},
  doi =		{10.4230/LIPIcs.IPEC.2015.270},
  annote =	{Keywords: block graph, polynomial kernel, single-exponential FPT algorithm}
}

Keywords: block graph, polynomial kernel, single-exponential FPT algorithm
Seminar: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 09.11.2015


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