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, Kn, on n vertices, and show how fast Walker-Maker can build desired spanning structures in these games.
We study the unbiased WalkerMaker-WalkerBreaker games on the edge set of the complete graph on n vertices, Kn, a variant of 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.
