Enumeration of Spanning Subgraphs with Degree Constraints
نویسنده
چکیده
For a finite undirected multigraph G = (V, E) and functions f, g : V → N, let N f (G, j) denote the number of (f, g)– factors of G with exactly j edges. The Heilmann-Lieb Theorem implies that ∑ j N 1 0 (G, j)t is a polynomial with only real (negative) zeros, and hence that the sequence N 0 (G, j) is strictly logarithmically concave. Separate generalizations of this theorem were obtained by Ruelle and by the author. We unify, simplify, and generalize these results by means of the Grace–Szegö–Walsh Coincidence Theorem.
منابع مشابه
Weighted enumeration of spanning subgraphs with degree constraints
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