Generating random graphs in biased Maker-Breaker games

We present a general approach connecting biased Maker-Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker-Breaker games. In particular, we show that for b = Θ( n lnn), playing a (1 : b) game on E(Kn), Maker can build a graph which contains copies of all spanning trees having maximum degree ∆ = O(1) with a bare path of linear length (a bare path in a tree T is a path with all interior vertices of degree exactly two in T ).