Perfect partition of some regular bipartite graphs
Abstract
A graph has a perfect partition if all its perfect matchings can be partitioned so that each part is a 1-factorization of the graph. Let Lrm, r=Krm,rm-mKr,r. We first give a formula to count the number of perfect matchings of Lrm, r, then show that L6,1 and L8,2 have perfect partitions.
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