Lecture Notes in Computer Science Volume 318, 1988, pp 233-242
Date: 30 May 2005

NC algorithms for computing the number of perfect matchings in K 3,3-free graphs and related problems

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Abstract

We show that the problem of computing the number of perfect matchings in K 3,3-free graphs is in NC. This stands in striking contrast with the #P-completeness of counting the number of perfect matchings in arbitrary graphs. As corollaries we obtain NC algorithms for checking if a given K 3,3-free graph has a perfect matching and if it has an EXACT MATCHING. Our result also opens up the possibility of obtaining an NC algorithm for finding a perfect matching in K 3,3-free graphs.

Work done while visiting AT&T Bell Labs during 1986–87. Supported in part by a PYI Award, with matching funds from AT&T Bell Labs.