NC algorithms for computing the number of perfect matchings in K3,3-free graphs and related problems

  • Vijay V. Vazirani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 318)

Abstract

We show that the problem of computing the number of perfect matchings in K3,3-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 K3,3-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 K3,3-free graphs.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Vijay V. Vazirani
    • 1
  1. 1.Computer Science DepartmentCornell UniversityUSA

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