Abstract
We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every 0≤γ≤1/2 we find a constant c = c(γ) 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 + γ)|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 + γ - o(1))|E| edges that does not contain a cycle of length at least cn.
Original language | English |
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Pages (from-to) | 284-296 |
Number of pages | 13 |
Journal | Journal of Graph Theory |
Volume | 70 |
Issue number | 3 |
DOIs | |
State | Published - 2012 |
Keywords
- long cycles
- pseudorandom digraphs
- resilience