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.MFCS.2018.29
URN: urn:nbn:de:0030-drops-96111
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9611/
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Gajarský, Jakub ; Král', Daniel

Recovering Sparse Graphs

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LIPIcs-MFCS-2018-29.pdf (0.5 MB)

Abstract

We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that G and H agree on all but f(d,k) vertices.
Our work is motivated by the first order model checking in graph classes that are first order interpretable in classes of sparse graphs. We derive as a corollary that if G is a graph class with bounded expansion, then the first order model checking is fixed parameter tractable in the class of all graphs that can obtained from a graph G in G by complementing on at most k arbitrary subsets of the vertex set of G; this implies an earlier result that the first order model checking is fixed parameter tractable in graph classes interpretable in classes of graphs with bounded maximum degree.

BibTeX - Entry

@InProceedings{gajarsk_et_al:LIPIcs:2018:9611,
  author =	{Jakub Gajarsk{\'y} and Daniel Kr{\'a}l'},
  title =	{{Recovering Sparse Graphs}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9611},
  URN =		{urn:nbn:de:0030-drops-96111},
  doi =		{10.4230/LIPIcs.MFCS.2018.29},
  annote =	{Keywords: model checking, degenerate graphs, interpretations, bounded expansion}
}

Keywords: model checking, degenerate graphs, interpretations, bounded expansion
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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