Graphical condensation of plane graphs: a combinatorial approach

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dc.creatorYan, Weigen
dc.creatorYeh, Yeong-Nan
dc.creatorZhang, Fuji
dc.date2005-09-15
dc.date2005-09-23
dc.date.accessioned2026-07-07T06:18:48Z
dc.date.available2026-07-07T06:18:48Z
dc.descriptionThe 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.
dc.description13 pages, 5 figures. accepted by Theoretial Computer Science
dc.identifierhttps://arxiv.org/abs/math/0509337
dc.identifierhttp://arxiv.org/abs/math/0509337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94862
dc.subjectCombinatorics
dc.subject05C70; 05C90
dc.titleGraphical condensation of plane graphs: a combinatorial approach
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