Embedding cycles of given length in oriented graphs
arXiv:1110.5669 · doi:10.1016/j.ejc.2012.10.002
Abstract
Kelly, Kuehn and Osthus conjectured that for any l>3 and the smallest number k>2 that does not divide l, any large enough oriented graph G with minimum indegree and minimum outdegree at least \lfloor |V(G)|/k\rfloor +1 contains a directed cycle of length l. We prove this conjecture asymptotically for the case when l is large enough compared to k and k>6. The case when k<7 was already settled asymptotically by Kelly, Kuehn and Osthus.
8 pages, 2 figures