Dominating set counting in graph classes

Authors:
Shuji Kijima;Yoshio Okamoto;Takeaki Uno
Affiliations:
Graduate School of Information Science and Electrical Engineering, Kyushu University, Japan;Center for Graduate Education Initiative, Japan Advanced Institute of Science and Technology, Japan;National Institute of Informatics, Japan
Venue:
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Year:
2011

Citing 4
Cited 0

Counting the number of independent sets in chordal graphs

Journal of Discrete Algorithms
Linear time algorithms for counting the number of minimal vertex covers with minimum/maximum size in an interval graph

Information Processing Letters
Counting the Number of Matchings in Chordal and Chordal Bipartite Graph Classes

Graph-Theoretic Concepts in Computer Science
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences

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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.