It is commonly believed that vertex-transitive graphs (and in particular Cayley graphs) tend to contain hamilton cycles. The only known connected vertex-transitive graphs without hamilton cycles are K ...

It would be interesting to find a vertex transitive graph whose matching polynomial has a nonsimple root. Such a graph would not have a hamiltonian path (see [1,2]) and would disprove a conjecture of ...

The Annals of Probability, Vol. 28, No. 3 (Jul., 2000), pp. 1111-1137 (27 pages) Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition ...

More precisely, we prove that For the Potts model on transitive graphs, correlations decay exponentially fast for β < βc. For the random-cluster model with cluster weight q ≥ 1 on transitive graphs, ...