Embedding cycles of given length in oriented graphs

作者：Kuehn Daniela; Osthus Deryk; Piguet Diana

来源：European Journal of Combinatorics, 2013, 34(2): 495-501.

DOI：10.1016/j.ejc.2012.10.002

Kelly, Kuhn and Osthus conjectured that for any l %26gt;= 4 and the smallest number k %26gt;= 3 that does not divide l, any large enough oriented graph G with delta(+)(G), delta(-)(G) %26gt;= (G) %26gt;= left perpendicular vertical bar V(G)vertical bar kright perpendicular + 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 %26gt;= 7. The case when k %26lt;= 6 was already settled asymptotically by Kelly, Kuhn and Osthus.

• 出版日期2013-2