On the WalkerMaker–WalkerBreaker games

Abstract

We study the unbiased WalkerMaker–WalkerBreaker games on the edge set of the complete graph on n vertices, Kn, a variant of the well-known Maker–Breaker positional games, where both players have the restriction on the way of playing. Namely, each player has to choose her/his edges according to a walk. Here, we focus on two standard graph games — the Connectivity game and the Hamilton cycle game and show how quickly WalkerMaker can win both games.