English

Embedding cycles of given length in oriented graphs

Combinatorics 2012-10-24 v2

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.

Keywords

Cite

@article{arxiv.1110.5669,
  title  = {Embedding cycles of given length in oriented graphs},
  author = {Daniela Kühn and Deryk Osthus and Diana Piguet},
  journal= {arXiv preprint arXiv:1110.5669},
  year   = {2012}
}

Comments

8 pages, 2 figures

R2 v1 2026-06-21T19:25:42.738Z