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.2015.365
URN: urn:nbn:de:0030-drops-55976
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5597/
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Sandeep, R. B. ; Sivadasan, Naveen

Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion

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Abstract

A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k^4) vertices was found by Fellows et. al. (Discrete Optimization, 2011).

In this paper, we give an improved kernel of O(k^3) vertices for Diamond-free Edge Deletion. We give an alternative proof of the NP-completeness of the problem and observe that it cannot be solved in time 2^{o(k)} * n^{O(1)}, unless the Exponential Time Hypothesis fails.

BibTeX - Entry

@InProceedings{sandeep_et_al:LIPIcs:2015:5597,
  author =	{R. B. Sandeep and Naveen Sivadasan},
  title =	{{Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{365--376},
  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/2015/5597},
  URN =		{urn:nbn:de:0030-drops-55976},
  doi =		{10.4230/LIPIcs.IPEC.2015.365},
  annote =	{Keywords: edge deletion problems, polynomial kernelization}
}

Keywords: edge deletion problems, polynomial kernelization
Collection: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 19.11.2015

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