Geodesic
Degree conditions forcing oriented cycles
Roman Glebov1 ; Andrzej Grzesik2 ; Jan Volec3 ; Roman Glebov ; Andrzej Grzesik ; Jan Volec
1Department of Mathematics, Ben Gurion University of the Negev, Beersheba, Israel
2Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
3Department of Mathematics, Emory University, Atlanta, USA
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 729-733 
Roman Glebov; Andrzej Grzesik; Jan Volec; Roman Glebov; Andrzej Grzesik; Jan Volec. Degree conditions forcing oriented cycles. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 729-733. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a57/
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     title = { Degree conditions forcing oriented cycles},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {729--733},
     year = {2019},
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Voir la notice de l'article provenant de la source Comenius University

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.