Graphical condensation of plane graphs: a combinatorial approach

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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.
13 pages, 5 figures. accepted by Theoretial Computer Science

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Combinatorics, 05C70; 05C90

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http://salesiana.dossiersoluciones.com/handle/123456789/94862

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509337
 http://arxiv.org/abs/math/0509337

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arXiv