On the P�sa-Seymour conjecture

Paul Seymour conjectured that any graph G of order n and minimum degree at least contains the kth power of a Hamilton cycle. We prove the following approximate version. For any ϵ ≥ 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least (k/k+1 + ε )n, then G contains the kth power of a Hamilton cycle.