TY - JOUR
T1 - Embedding cycles of given length in oriented graphs
AU - Kühn, D.
AU - Osthus, D.
AU - Piguet, D.
N1 - Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2013/2/1
Y1 - 2013/2/1
N2 - Kelly, Kühn and Osthus conjectured that for any ℓ ≥ 4 and the smallest number k ≥ 3 that does not divideℓ, any large enough oriented graphG with δ (G), δ (G) ≥ {pipe} V (G) {pipe} / k + 1 contains a directed cycle of lengthℓ. We prove this conjecture asymptotically for the case whenℓ is large enough compared to k and k ≥ 7. The case whenk ≤ 6 was already settled asymptotically by Kelly, Kühn and Osthus.
AB - Kelly, Kühn and Osthus conjectured that for any ℓ ≥ 4 and the smallest number k ≥ 3 that does not divideℓ, any large enough oriented graphG with δ (G), δ (G) ≥ {pipe} V (G) {pipe} / k + 1 contains a directed cycle of lengthℓ. We prove this conjecture asymptotically for the case whenℓ is large enough compared to k and k ≥ 7. The case whenk ≤ 6 was already settled asymptotically by Kelly, Kühn and Osthus.
UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84867957626&md5=242c50b88d3eac0de6bddf753f3d0a96
U2 - 10.1016/j.ejc.2012.10.002
DO - 10.1016/j.ejc.2012.10.002
M3 - Article
AN - SCOPUS:84867957626
VL - 34
SP - 495
EP - 501
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
IS - 2
ER -