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Enumeration of spanning subgraphs with degree constraints | | David G. Wagner
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2 Dec 2004 | | Subject: | Combinatorics MSC-class: 05A20; 05C30, 26C10, 30C15 | math.CO | | Abstract: | For a finite undirected multigraph G=(V,E) and functions f,g:V-->NN, let N_f^g(G,j) denote the number of (f,g)-factors of G with exactly j edges. The Heilmann-Lieb Theorem implies that sum_j N_0^1(G,j) t^j is a polynomial with only real (negative) zeros, and hence that the sequence {N_0^1(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. | | Source: | arXiv, math.CO/0412059 | | Services: | Forum | Review | PDF | Favorites | |
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