Abstract
Laszlo Lovasz recently posed the following problem: “Is there an NC algorithm for testing if a given graph has a unique perfect matching.” We present such an NC algorithm. The ideas developed may be a step towards obtaining an NC algorithm for determining if a graph has a perfect matching. We also give NC algorithms for obtaining a transitive orientation for a comparability graph, anad an interval representation for an interval graph. These enable us to obtain an NC algorithm for finding a maximum matching in incomparability graphs.
Supported by NSF Grant MCS 82-04506, and an IBM Graduate Fellowship.
Supported by NSF Grant BCR 85-03611, and an IBM Faculty Development Award.
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© 1985 Springer-Verlag Berlin Heidelberg
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Kozen, D., Vazirani, U.V., Vazirani, V.V. (1985). NC algorithms for comparability graphs, interval graphs, and testing for unique perfect matching. In: Maheshwari, S.N. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1985. Lecture Notes in Computer Science, vol 206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16042-6_28
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DOI: https://doi.org/10.1007/3-540-16042-6_28
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