Local Resilience of Almost Spanning Trees in Random Graphs

We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Lovasz Local Lemma which can dramatically reduce the number of edges needed in a dependency graph when there is an ordering underlying the significant dependencies of events. This appears to represent the first successful application of a Local Lemma to games. (C) 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 140-161, 2011