Long cycles in subgraphs of (pseudo)random directed graphs

Ido Ben-Eliezer*, Michael Krivelevich, Benny Sudakov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)284-296
Number of pages13
JournalJournal of Graph Theory
Issue number3
StatePublished - 2012


  • long cycles
  • pseudorandom digraphs
  • resilience


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