Graphical condensation of plane graphs: a combinatorial approach
Abstract
The method of graphical vertex-condensation for enumerating perfect matchings of plane bipartite graph was found by Propp (Theoret. Comput. Sci. 303(2003), 267-301), and was generalized by Kuo (Theoret. Comput. Sci. 319 (2004), 29-57) and Yan and Zhang (J. Combin. Theory Ser. A, 110(2005), 113-125). In this paper, by a purely combinatorial method some explicit identities on graphical vertex-condensation for enumerating perfect matchings of plane graphs (which do not need to be bipartite) are obtained. As applications of our results, some results on graphical edge-condensation for enumerating perfect matchings are proved, and we count the sum of weights of perfect matchings of weighted Aztec diamond.
Keywords
Cite
@article{arxiv.math/0509337,
title = {Graphical condensation of plane graphs: a combinatorial approach},
author = {Weigen Yan and Yeong-Nan Yeh and Fuji Zhang},
journal= {arXiv preprint arXiv:math/0509337},
year = {2007}
}
Comments
13 pages, 5 figures. accepted by Theoretial Computer Science