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Hitting forbidden subgraphs in graphs of bounded treewidth

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Cygan, Marek, Marx, Daniel, Pilipczuk, Marcin and Pilipczuk, Michał (2014) Hitting forbidden subgraphs in graphs of bounded treewidth. In: Csuhaj-Varjú, E. and Dietzfelbinger, Martin and Ésik, Zoltán, 1951-, (eds.) Mathematical foundations of computer science 2014 : proceedings, Part II 39th International Symposium, MFCS 2014, Budapest, Hungary, August 25-29, 2014. Lecture Notes in Computer Science (Volume 8635). Berlin ; London: Springer Verlag, pp. 189-200. ISBN 9783662444641

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Official URL: http://dx.doi.org/10.1007/978-3-662-44465-8_17

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Abstract

We study the complexity of a generic hitting problem H -Subgraph Hitting , where given a fixed pattern graph H and an input graph G, we seek for the minimum size of a set X ⊆ V(G) that hits all subgraphs of G isomorphic to H. In the colorful variant of the problem, each vertex of G is precolored with some color from V(H) and we require to hit only H-subgraphs with matching colors. Standard techniques (e.g., Courcelle’s theorem) show that, for every fixed H and the problem is fixed-parameter tractable parameterized by the treewidth of G; however, it is not clear how exactly the running time should depend on treewidth. For the colorful variant, we demonstrate matching upper and lower bounds showing that the dependence of the running time on treewidth of G is tightly governed by μ(H), the maximum size of a minimal vertex separator in H. That is, we show for every fixed H that, on a graph of treewidth t, the colorful problem can be solved in time 2O(tμ(H))⋅|V(G)|, but cannot be solved in time 2o(tμ(H))⋅|V(G)|O(1), assuming the Exponential Time Hypothesis (ETH). Furthermore, we give some preliminary results showing that, in the absence of colors, the parameterized complexity landscape of H -Subgraph Hitting is much richer.

Item Type: Book Item
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Graph theory, Computational complexity
Series Name: Lecture Notes in Computer Science
Publisher: Springer Verlag
Place of Publication: Berlin ; London
ISBN: 9783662444641
ISSN: 0302-9743
Book Title: Mathematical foundations of computer science 2014 : proceedings, Part II 39th International Symposium, MFCS 2014, Budapest, Hungary, August 25-29, 2014
Editor: Csuhaj-Varjú, E. and Dietzfelbinger, Martin and Ésik, Zoltán, 1951-
Official Date: 2014
Dates:
DateEvent
2014UNSPECIFIED
Date of first compliant deposit: 28 December 2015
Number: Volume 8635
Number of Pages: 12
Page Range: pp. 189-200
DOI: 10.1007/978-3-662-44465-8_17
Status: Peer Reviewed
Publication Status: Published
Description:
Funder: Seventh Framework Programme (European Commission) (FP7), European Research Council (ERC), Országos Tudományos Kutatási Alapprogramok (OTKA), Narodowe Centrum Nauki (NCN)
Grant number: 267959 (ERC), 280152 (ERC), NK10564 (OTKA), DEC-2012/05/D/ST6/03214 (NCN)

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