# NC algorithms for computing the number of perfect matchings in *K*_{3,3}-free graphs and related problems

Conference paper

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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.

## Keywords

Planar Graph Perfect Match Parallel Algorithm Polynomial Time Algorithm Decomposition Tree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1988