The variety of transitive graphs contributed to the difficulty of proving Schramm’s locality conjecture. In the 15 years between Schramm’s conjecture and Easo and Hutchcroft’s proof, various groups of ...

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 ...