Lower bounds for partial matchings in regular bipartite graphs and applications to the monomer–dimer entropy

Authors:
Shmuel Friedland;Leonid Gurvits
Affiliations:
Department of mathematics, statistics and computer science, university of illinois at chicago, chicago, illinois 60607-7045, usa (e-mail: friedlan@uic.edu);Los alamos national laboratories, los alamos, nm 87545, usa (e-mail: gurvits@lanl.gov)
Venue:
Combinatorics, Probability and Computing
Year:
2008

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Abstract

We derive here the Friedland–Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in r-regular bipartite graphs. It is shown that some of these bounds are asymptotically sharp. We improve the known lower bound for the three-dimensional monomer–dimer entropy.