  We study the unbiased WalkerMaker-WalkerBreaker games on the edge set of the
complete graph on $n$ vertices, $K_n$, 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.
