Maker–Breaker Games with Constraints

Abstract

We analyse the unbiased WalkerMaker–WalkerBreaker game, a variant of the well-known Maker–Breaker positional game where both players Maker and Breaker are constrained to choose their edges according to a walk. Here, we consider two standard graph games - the Connectivity game and the Hamilton Cycle game played on the edge set of the complete graph, \(K_n\), on n vertices, and show how fast WalkerMaker can build desired spanning structures in these games.