A Reduction Theorem for Perfect Matchings of Graphs Having a Cellular Completion
نویسنده
چکیده
A cellular graph is a graph whose edges can be partitioned into 4-cycles (called cells) so that each vertex is containedin at most two cells. We present a \ReductionTheorem" for the number of matchingsof certain subgraphs of cellular graphs. This generalizesthe main result of Ci1]. As applications of the Reduction Theorem we obtain a new proof of Stanley's multivariate version of the Aztec diamond theorem, a weighted generalization of a result of Knuth Kn] concerning spanning trees of Aztec diamond graphs, a combinatorial proof of Yang's enumeration Y] of matchings of fortress graphs and direct proofs for certain identities of Jockusch and Propp JP].
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