Parameterized complexity of induced H-matching on claw-free graphs

Danny Hermelin; Matthias Mnich; Erik Jan Van Leeuwen

doi:10.1007/978-3-642-33090-2_54

Parameterized complexity of induced H-matching on claw-free graphs

Danny Hermelin, Matthias Mnich, Erik Jan Van Leeuwen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

The Induced H -Matching problem asks to find k disjoint, induced subgraphs isomorphic to H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes amongst others the classical Independent Set and Induced Matching problems. We show that Induced H -Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph of constant size, and even admits a polynomial kernel when H is a clique. Both results rely on a new, strong algorithmic structure theorem for claw-free graphs. To show the fixed-parameter tractability of the problem, we additionally apply the color-coding technique in a nontrivial way. Complementing the above two positive results, we prove the W[1]-hardness of Induced H -Matching for graphs excluding K _1,4 as an induced subgraph. In particular, we show that Independent Set is W[1]-hard on K _1,4-free graphs.

Original language	English
Title of host publication	Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings
Pages	624-635
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-33090-2_54
State	Published - 1 Oct 2012
Externally published	Yes
Event	20th Annual European Symposium on Algorithms, ESA 2012 - Ljubljana, Slovenia Duration: 10 Sep 2012 → 12 Sep 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7501 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th Annual European Symposium on Algorithms, ESA 2012
Country/Territory	Slovenia
City	Ljubljana
Period	10/09/12 → 12/09/12

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-33090-2_54

Cite this

Hermelin, D., Mnich, M., & Van Leeuwen, E. J. (2012). Parameterized complexity of induced H-matching on claw-free graphs. In Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings (pp. 624-635). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7501 LNCS). https://doi.org/10.1007/978-3-642-33090-2_54

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abstract = "The Induced H -Matching problem asks to find k disjoint, induced subgraphs isomorphic to H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes amongst others the classical Independent Set and Induced Matching problems. We show that Induced H -Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph of constant size, and even admits a polynomial kernel when H is a clique. Both results rely on a new, strong algorithmic structure theorem for claw-free graphs. To show the fixed-parameter tractability of the problem, we additionally apply the color-coding technique in a nontrivial way. Complementing the above two positive results, we prove the W[1]-hardness of Induced H -Matching for graphs excluding K 1,4 as an induced subgraph. In particular, we show that Independent Set is W[1]-hard on K 1,4-free graphs.",

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Hermelin, D, Mnich, M & Van Leeuwen, EJ 2012, Parameterized complexity of induced H-matching on claw-free graphs. in Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7501 LNCS, pp. 624-635, 20th Annual European Symposium on Algorithms, ESA 2012, Ljubljana, Slovenia, 10/09/12. https://doi.org/10.1007/978-3-642-33090-2_54

Parameterized complexity of induced H-matching on claw-free graphs. / Hermelin, Danny; Mnich, Matthias; Van Leeuwen, Erik Jan.
Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings. 2012. p. 624-635 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7501 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Parameterized complexity of induced H-matching on claw-free graphs

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