We study analogues of $mathcal{F}$-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. We examine analogous games on directed graphs, and show tight results on the walk-avoiding game. We also examine an
intermediate game played on undirected graphs, such that there exists an orientation avoiding a given family of directed graphs, and show bounds on the score. This last game is shown to be equivalent to a recent game studied by Hefetz, Krivelevich, Naor and Stojakovic, and we give new bounds for bias
We study F-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We sh
ow lower bounds on the length of path-avoiding games, and more precise results for short paths. We show sharp results for the tree avoiding game and the star avoiding game.
