P. Csikvári

activity

20122025

most citedMatching measure, Benjamini-Schramm convergence and the monomer-dimer free energy

14 citations · 31 across the 11 of their papers we have counts for

collaborators

Showing 2014Show all

4 papers · 1 filter

math.CO2014

The Density Turán problem

Péter Csikvári, Zoltán Lóránt Nagy

Let $H$ be a graph on $n$ vertices and let the blow-up graph $G [H]$ be defined as follows. We replace each vertex $v_{i}$ of $H$ by a cluster $A_{i}$ and connect some pairs of vertices…

math.CO2014

Matchings in vertex-transitive bipartite graphs

Péter Csikvári

A theorem of A. Schrijver asserts that a $d$ -regular bipartite graph on $2 n$ vertices has at least $(\frac{( d - 1 ) ^{d - 1}}{d ^{d - 2}})^{n}$ perfect matchings. L. Gurvits gave…

math.CO2014

Lower matching conjecture, and a new proof of Schrijver's and Gurvits's theorems

Péter Csikvári

Friedland's Lower Matching Conjecture asserts that if $G$ is a $d$ --regular bipartite graph on $v (G) = 2 n$ vertices, and $m_{k} (G)$ denotes the number of matchings of size $k$ , then $$…

math-ph2014★ 14 cited

Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy

Miklós Abért, Péter Csikvári, Tamás Hubai

We define the matching measure of a lattice L as the spectral measure of the tree of self-avoiding walks in L. We connect this invariant to the monomer-dimer partition function of…