On the Validations of the Asymptotic Matching Conjectures
2008 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 133, no 3, 513-533 p.Article in journal (Refereed) Published
In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer 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 is an element of[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.
Place, publisher, year, edition, pages
2008. Vol. 133, no 3, 513-533 p.
Matching and asymptotic growth of average matchings for r-regular, bipartite graphs, Monomer-dimer partitions and entropies, monomer-dimer problem, regular bipartite graphs, series-expansion, lattice, entropy, number, matrices, systems
IdentifiersURN: urn:nbn:se:kth:diva-17911DOI: 10.1007/s10955-008-9550-yISI: 000260376300006ScopusID: 2-s2.0-54949158545OAI: oai:DiVA.org:kth-17911DiVA: diva2:335956
QC 201005252010-08-052010-08-05Bibliographically approved