Hamilton cycles in dense vertex-transitive graphs
arXiv:1008.2193 · doi:10.1016/j.jctb.2014.05.001
Abstract
A famous conjecture of Lovász states that every connected vertex-transitive graph contains a Hamilton path. In this article we confirm the conjecture in the case that the graph is dense and sufficiently large. In fact, we show that such graphs contain a Hamilton cycle and moreover we provide a polynomial time algorithm for finding such a cycle.
26 pages, 3 figures; referees' comments incorporated; accepted for publication in Journal of Combinatorial Theory, series B