Dominating set counting in graph classes

Shuji Kijima; Yoshio Okamoto; Takeaki Uno

doi:10.1007/978-3-642-22685-4_2

Dominating set counting in graph classes

Shuji Kijima, Yoshio Okamoto, Takeaki Uno

Mathematical Informatics

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

7 Citations (Scopus)

Abstract

We make an attempt to understand the dominating set counting problem in graph classes from the viewpoint of polynomial-time computability. We give polynomial-time algorithms to count the number of dominating sets (and minimum dominating sets) in interval graphs and trapezoid graphs. They are based on dynamic programming. With the help of dynamic update on a binary tree, we further reduce the time complexity. On the other hand, we prove that counting the number of dominating sets (and minimum dominating sets) in split graphs and chordal bipartite graphs is #P-complete. These results are in vivid contrast with the recent results on counting the independent sets and the matchings in chordal graphs and chordal bipartite graphs.

Original language	English
Title of host publication	Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings
Pages	13-24
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-22685-4_2
Publication status	Published - Aug 29 2011
Event	17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States Duration: Aug 14 2011 → Aug 16 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6842 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	17th Annual International Computing and Combinatorics Conference, COCOON 2011
Country	United States
City	Dallas, TX
Period	8/14/11 → 8/16/11

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-22685-4_2

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Cite this

Kijima, S., Okamoto, Y., & Uno, T. (2011). Dominating set counting in graph classes. In Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings (pp. 13-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS). https://doi.org/10.1007/978-3-642-22685-4_2

Dominating set counting in graph classes. / Kijima, Shuji; Okamoto, Yoshio; Uno, Takeaki.

Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. p. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS).

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

Kijima, S, Okamoto, Y & Uno, T 2011, Dominating set counting in graph classes. in Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6842 LNCS, pp. 13-24, 17th Annual International Computing and Combinatorics Conference, COCOON 2011, Dallas, TX, United States, 8/14/11. https://doi.org/10.1007/978-3-642-22685-4_2

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