Domination when the stars are out

Danny Hermelin; Matthias Mnich; Erik Jan Van Leeuwen; Gerhard J. Woeginger

doi:10.1007/978-3-642-22006-7_39

Domination when the stars are out

Danny Hermelin, Matthias Mnich, Erik Jan Van Leeuwen, Gerhard J. Woeginger

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

Abstract

We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K _1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K _1,ℓ-free graphs and show that the problem is fixed-parameter tractable if and only if ℓ ≤ 3. Finally, we show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw-free graphs.

Original language	American English
Title of host publication	Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
Pages	462-473
Number of pages	12
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-642-22006-7_39
State	Published - 11 Jul 2011
Externally published	Yes
Event	38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland Duration: 4 Jul 2011 → 8 Jul 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	6755 LNCS

Conference

Conference	38th International Colloquium on Automata, Languages and Programming, ICALP 2011
Country/Territory	Switzerland
City	Zurich
Period	4/07/11 → 8/07/11

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-22006-7_39

Cite this

Hermelin, D., Mnich, M., Van Leeuwen, E. J., & Woeginger, G. J. (2011). Domination when the stars are out. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings (PART 1 ed., pp. 462-473). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-22006-7_39

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abstract = "We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K 1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K 1,ℓ-free graphs and show that the problem is fixed-parameter tractable if and only if ℓ ≤ 3. Finally, we show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw-free graphs.",

author = "Danny Hermelin and Matthias Mnich and {Van Leeuwen}, {Erik Jan} and Woeginger, {Gerhard J.}",

year = "2011",

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doi = "10.1007/978-3-642-22006-7_39",

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Hermelin, D, Mnich, M, Van Leeuwen, EJ & Woeginger, GJ 2011, Domination when the stars are out. in Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6755 LNCS, pp. 462-473, 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, Zurich, Switzerland, 4/07/11. https://doi.org/10.1007/978-3-642-22006-7_39

Domination when the stars are out. / Hermelin, Danny; Mnich, Matthias; Van Leeuwen, Erik Jan et al.
Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1. ed. 2011. p. 462-473 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1).

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

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T1 - Domination when the stars are out

AU - Hermelin, Danny

AU - Mnich, Matthias

AU - Van Leeuwen, Erik Jan

AU - Woeginger, Gerhard J.

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N2 - We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K 1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K 1,ℓ-free graphs and show that the problem is fixed-parameter tractable if and only if ℓ ≤ 3. Finally, we show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw-free graphs.

AB - We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K 1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K 1,ℓ-free graphs and show that the problem is fixed-parameter tractable if and only if ℓ ≤ 3. Finally, we show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw-free graphs.

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Hermelin D, Mnich M, Van Leeuwen EJ, Woeginger GJ. Domination when the stars are out. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 ed. 2011. p. 462-473. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-642-22006-7_39

Domination when the stars are out

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