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The longstanding Caccetta-Häggkvist Conjecture is asking for the minimum outdegree (or semidegree) in an oriented graph that forces the appearance of a directed cycle of a bounded length. Motivated by this, Kelly, Kühn and Osthus made a conjecture on the minimal semidegree forcing the appearance of a directed cycle of a given length, and proved it for cycles of length not divisible by 3. Here we prove all the remaining cases of their conjecture with the optimal semidegree threshold.
How to Cite
Glebov, R., Grzesik, A., & Volec, J. (2019). Degree conditions forcing oriented cycles. Acta Mathematica Universitatis Comenianae, 88(3), 729-733. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1291/719