Long cycles in subgraphs of (pseudo)random directed graphs
We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every 08?81/2 we find a constant c = c(?) such that the following holds. Let G = (V, E) be a (pseudo)random directed graph on n vertices and with at least a linear number of edges, and let G? be a subgraph of G with (1/2 + ?)|E| edges. Then G? contains a directed cycle of length at least (c ? o(1))n. Moreover, there is a subgraph G??of G with (1/2 + ? ? o(1))|E| edges that does not contain a cycle of length at least cn.  2011 Wiley Periodicals, Inc. J Graph Theory 70: 284296, 2012
long cycles resilience pseudorandom digraphs