On the Number of Group-Weighted Matchings
نویسنده
چکیده
Let G be a bipartite graph with a bicoloration {A, B}, |A| = |B|, and let w : E(G) → K where K is a finite abelian group with k elements. For a subset S ⊆ E(G) let w(S) = ∏e∈S w(e). A perfect matching M ⊆ E(G) is a w-matching if w(M) = 1. It is shown that if deg(a) ≥ d for all a ∈ A, then either G has no w-matchings, or G has at least (d − k + 1)! w-matchings.
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