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Date:
30 May 2005
NC algorithms for computing the number of perfect matchings in K _{3,3}free graphs and related problems
 Vijay V. Vazirani
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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 #Pcompleteness 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.
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 Title
 NC algorithms for computing the number of perfect matchings in K _{3,3}free graphs and related problems
 Book Title
 SWAT 88
 Book Subtitle
 1st Scandinavian Workshop on Algorithm Theory Halmstad, Sweden, July 5–8, 1988 Proceedings
 Pages
 pp 233242
 Copyright
 1988
 DOI
 10.1007/3540194878_27
 Print ISBN
 9783540194873
 Online ISBN
 9783540392880
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 318
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Authors

 Vijay V. Vazirani ^{(1)}
 Author Affiliations

 1. Computer Science Department, Cornell University, USA
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