Enumeration of spanning subgraphs with degree constraints
Combinatorics
2007-05-23 v2
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-Szeg\"o-Walsh Coincidence Theorem.
Cite
@article{arxiv.math/0412059,
title = {Enumeration of spanning subgraphs with degree constraints},
author = {David G. Wagner},
journal= {arXiv preprint arXiv:math/0412059},
year = {2007}
}
Comments
15 pages. minor corrections and a new result