Szemerédi's regularity lemma for sparse graphs
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extremal Graph Theory
Random Structures & Algorithms
Resilient Pancyclicity of Random and Pseudorandom Graphs
SIAM Journal on Discrete Mathematics
Local resilience of almost spanning trees in random graphs
Random Structures & Algorithms
Local resilience and hamiltonicity maker–breaker games in random regular graphs
Combinatorics, Probability and Computing
Bandwidth theorem for random graphs
Journal of Combinatorial Theory Series B
Dirac's theorem for random graphs
Random Structures & Algorithms
| Hi-index | 0.00 |
We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every 08γ81/2 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. © 2011 Wiley Periodicals, Inc. J Graph Theory, © 2012 Wiley Periodicals, Inc. (Contract grant sponsors: ERC (to I. B.); USA-Israel BSF; Israel Science Foundation; Contract grant numbers: 2006322; 1063/08 (to M. K.); Contract grant sponsors: NSF grant DMS-1101185; NSF CAREER award DMS-0812005; USA-Israeli BSF.)