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.
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© 1988 Springer-Verlag Berlin Heidelberg
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Vazirani, V.V. (1988). NC algorithms for computing the number of perfect matchings in K 3,3-free graphs and related problems. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_27
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DOI: https://doi.org/10.1007/3-540-19487-8_27
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