On the validations of the Asymptotic Matching Conjectures
نویسندگان
چکیده
In this paper we review the asymptotic matching conjectures for rregular bipartite graphs, and their connections in estimating the monomerdimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p ∈ [0, 1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs. 2000 Mathematics Subject Classification: 05A15, 05A16, 05C70, 05C80, 82B20
منابع مشابه
Validations of the Asymptotic Matching Conjectures
In this paper we review the asymptotic matching conjectures for rregular bipartite graphs, and their connections in estimating the monomerdimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graph...
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