Fast exponential-time algorithms for the forest counting in graph classes

Authors:
Heidi Gebauer;Yoshio Okamoto
Affiliations:
ETH Zurich, Zurich, Switzerland;Toyohashi University of Technology, Tempaku, Toyohashi, Aichi, Japan
Venue:
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Year:
2007

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Abstract

We prove #P-completeness for counting the number of forests in regular graphs and chordal graphs. We also present algorithms for this problem, running in O* (1.8494m) time for 3-regular graphs, and O* (1.9706m) time for unit interval graphs, where m is the number of edges in the graph and O*-notation ignores a polynomial factor. The algorithms can be generalized to the Tutte polynomial computation.