Cycle lengths in graphs with large minimum degree
Our 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: i. G contains a cycle of length t for every even integer t ∈ [4, δ(G) + 1]. ii. 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.
Journal of Graph Theory
Nikiforov, V., & Schelp, R. (2006). Cycle lengths in graphs with large minimum degree. Journal of Graph Theory, 52 (2), 157-170. https://doi.org/10.1002/jgt.20151