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 ...

We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected ...

where the sum runs from 0 to [n/2]. It is known that every matching polynomial has only real roots. See [1,2]. It would be interesting to find a vertex transitive graph whose matching polynomial has a ...

Advances in Applied Probability, Vol. 24, No. 4 (Dec., 1992), pp. 845-857 (13 pages) A three-parameter model of a random directed graph (digraph) is specified by the ...