On the number of matchings in regular graphs
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Publication:1010842
zbMath1181.05011arXiv0801.2256MaRDI QIDQ1010842
Shmuel Friedland, Klas Markström, Elliot Krop
Publication date: 7 April 2009
Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0801.2256
Random graphs (graph-theoretic aspects) (05C80) Exact enumeration problems, generating functions (05A15) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Asymptotic enumeration (05A16)
Related Items (18)
Positivity of the virial coefficients in lattice dimer models and upper bounds on the number of matchings on graphs ⋮ Counting matchings via capacity-preserving operators ⋮ Lower matching conjecture, and a new proof of Schrijver's and Gurvits's theorems ⋮ Matchings in regular graphs: minimizing the partition function ⋮ A mysterious cluster expansion associated to the expectation value of the permanent of \(0\)-\(1\) matrices ⋮ \(1/n\) expansion for the number of matchings on regular graphs and Monomer-Dimer entropy ⋮ Results and questions on matchings in abelian groups and vector subspaces of fields ⋮ Asymptotics of the upper matching conjecture ⋮ Spectral moments of regular graphs in terms of subgraph counts ⋮ Statistical Matching Theory ⋮ Upper bounds on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges ⋮ A proof of the upper matching conjecture for large graphs ⋮ Matchings in vertex-transitive bipartite graphs ⋮ A positivity property of the dimer entropy of graphs ⋮ Tight bounds on the coefficients of partition functions via stability ⋮ Matchings in Benjamini–Schramm convergent graph sequences ⋮ Tight bounds on the coefficients of partition functions via stability ⋮ Covers, orientations and factors
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