Group Weighted Matchings in Bipartite Graphs
نویسنده
چکیده
Let G be a bipartite graph with 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 c E(G) let w(S) = IIeE s (e).A Perfect matching M c E(G) is a w-matching if w(M) = 1. A characterization is given for all w's for which every perfect matching is a w-matching. It is shown that if G = Kk+1,k+1 then either G has no w-matchings or it has at least 2 m-matchings. If K is the group of order 2 and deg(a) > d for all a e A, then either G has no w-matchings, or G has at least (d — 1)! w-matchings.
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