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

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	American 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

Conference

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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

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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N2 - 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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Parameterized complexity of induced H-matching on claw-free graphs

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