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Recovering sparse graphs

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Gajarsky, Jakub and Králʼ, Daniel (2018) Recovering sparse graphs. Leibniz International Proceedings in Informatics (LIPIcs), 117 . 29:1-29:15. 29. doi:10.4230/LIPIcs.MFCS.2018.29

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Official URL: https://doi.org/10.4230/LIPIcs.MFCS.2018.29

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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 ϵ 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.

Item Type: Journal Item
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Graph algorithms, Finite model theory
Series Name: Leibniz International Proceedings in Informatics (LIPIcs)
Journal or Publication Title: Leibniz International Proceedings in Informatics (LIPIcs)
Publisher: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
ISBN: 9783959770866
ISSN: 1868-8969
Official Date: 2018
Dates:
DateEvent
2018Published
13 June 2018UNSPECIFIED
Volume: 117
Page Range: 29:1-29:15
Article Number: 29
DOI: 10.4230/LIPIcs.MFCS.2018.29
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
648527H2020 European Research Councilhttp://dx.doi.org/10.13039/100010663
648509H2020 European Research Councilhttp://dx.doi.org/10.13039/100010663
Conference Paper Type: Paper
Title of Event: MFCS'18
Type of Event: Conference
Location of Event: Liverpool
Date(s) of Event: 27-31 August 2018
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