On the Validations of the Asymptotic Matching Conjectures

  title={On the Validations of the Asymptotic Matching Conjectures},
  author={S. Friedland and E. Krop and P. H. Lundow and K. Markstr{\"o}m},
  journal={Journal of Statistical Physics},
  • S. Friedland, E. Krop, +1 author K. Markström
  • Published 2006
  • Mathematics, Physics
  • Journal of Statistical Physics
  • 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∈[0,1], for… CONTINUE READING
    35 Citations

    Figures from this paper

    Results and open problems in matchings in regular graphs
    • 2
    • PDF
    Matchings and independent sets of a fixed size in regular graphs
    • 32
    • PDF
    A proof of the Upper Matching Conjecture for large graphs
    • 2
    • PDF
    Asymptotics of the Upper Matching Conjecture
    • 11
    • PDF
    Extremal and probabilistic results for regular graphs
    • Highly Influenced
    • PDF
    Independent sets, matchings, and occupancy fractions
    • 36
    • PDF


    Generalized Friedland-Tverberg inequality: applications and extensions
    • 13
    • PDF
    On the Number of Matchings in Regular Graphs
    • 45
    • PDF
    The Statistics of Dimers on a Lattice
    • 504
    Counting 1-Factors in Regular Bipartite Graphs
    • A. Schrijver
    • Computer Science, Mathematics
    • J. Comb. Theory, Ser. B
    • 1998
    • 118
    • PDF