Cycle lengths in graphs with large minimum degree

Abstract

AbstractOur main result is the following theorem.Let k ≥ 2 be an integer, G be a graph of sufficiently large order n, and δ(G) ≥ n/k. Then: G contains a cycle of length t for every even integer t ∈ [4, δ(G) + 1]. If G is nonbipartite then G contains a cycle of length t for every odd integer t ∈ [2k − 1, δ(G) + 1], unless k ≥ 6 and G belongs to a known exceptional class. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 157–170, 2006