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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
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 | |||||||||
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| 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: |
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| 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: |
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| 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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| Open Access Version: |
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