Long cycles in random subgraphs of graphs with large minimum degree
Let G be any graph of minimum degree at least k, and let Gp be the random subgraph of G obtained by keeping each edge independently with probability p. Recently, Krivelevich, Lee and Sudakov showed that if pk ? then with probability tending to 1 Gp contains a cycle of length at least (1  o(1))k. We give a much shorter proof of this result, also based on depth-first search.  2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 764767, 2014
long cycles random graphs