Lovász's Hamiltonicity conjecture for vertex-transitive graphs

A graph is vertex transitive if, for every pair of vertices $v,w$, there is a graph automorphism mapping $v$ to $w$. A graph is Hamiltonian if it admits a Hamiltonian circuit, namely a simple circuit containing every vertex of the graph. Lovász's conjecture. All but a finite number of vertex-transitive graphs are Hamiltonian. It remains open whether the remaining odd graphs are Hamiltonian; this conjecture is therefore unresolved in general.