Mathematics – Combinatorics
Scientific paper
2006-02-28
Mathematics
Combinatorics
25 pages, 9 figures
Scientific paper
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 $p\in [0,1]$, for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite $r$-regular bipartite graphs.
Friedland Shmuel
Krop Elliot
Lundow Per Hakan
Markström Klas
No associations
LandOfFree
Validations of the Asymptotic Matching Conjectures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Validations of the Asymptotic Matching Conjectures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Validations of the Asymptotic Matching Conjectures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-550183