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2014 IEEE Conference on Computational Complexity (CCC) (2014)
Vancouver, BC, Canada
June 11, 2014 to June 13, 2014
ISSN: 1093-0159
ISBN: 978-1-4799-3626-7
pp: 66-77
ABSTRACT
Counting the number of perfect matchings in arbitrary graphs is a sharpP-complete problem. However, for some restricted classes of graphs the problem can be solved efficiently. In the case of planar graphs, and even for K_{3, 3}-free graphs, Vazirani showed that it is in NC^2. The technique there is to compute a Pfaffian orientation of a graph. In the case of K_5-free graphs, this technique will not work because some K_5-free graphs do not have a Pfaffian orientation. We circumvent this problem and show that the number of perfect matchings in K_5-free graphs can be computed in polynomial time and we describe a circuit construction in TC2.
INDEX TERMS
Vectors, Law, Polynomials, Educational institutions, Heuristic algorithms, Computer science
CITATION

S. Straub, T. Thierauf and F. Wagner, "Counting the Number of Perfect Matchings in K5-Free Graphs," 2014 IEEE Conference on Computational Complexity (CCC), Vancouver, BC, Canada, 2014, pp. 66-77.
doi:10.1109/CCC.2014.15
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