文章基本信息

标题：Recovering Sparse Graphs
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作者：Jakub Gajarsk{\'y ; Daniel Kr{\'a}l
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：117
页码：1-15
DOI：10.4230/LIPIcs.MFCS.2018.29
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：model checking; degenerate graphs; interpretations; bounded expansion