Graphical condensation of plane graphs: A combinatorial approach
نویسندگان
چکیده
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), 113125). 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.
منابع مشابه
Graphical Condensation Generalizations Involving Pfaffians and Determinants
Graphical condensation is a technique used to prove combinatorial identities among numbers of perfect matchings of plane graphs. Propp and Kuo first applied this technique to prove identities for bipartite graphs. Yan, Yeh, and Zhang later applied graphical condensation to nonbipartite graphs to prove more complex identities. Here we generalize some of the identities of Yan, Yeh, and Zhang. We ...
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We present some Pfaffian identities, which are completely different from the Plücker relations. As consequences we obtain a quadratic identity for the number of perfect matchings of plane graphs, which has a simpler form than the formula by Yan et al (Graphical condensation of plane graphs: a combinatorial approach, Theoret. Comput. Sci., to appear), and we also obtain some new determinant iden...
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The method of graphical condensation for enumerating perfect matchings was found by Propp (Theoretical Computer Science 303(2003), 267-301), and was generalized by Kuo (Theoretical Computer Science 319 (2004), 29-57). In this paper, we obtain some more general results on graphical condensation than Kuo’s. Our method is also different from Kuo’s. As applications of our results, we obtain a new p...
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 349 شماره
صفحات -
تاریخ انتشار 2005