FF-saturation games

We study FF-saturation games, first introduced by Füredi, Reimer and Seress in 1991, and named as such by West (2009). The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We show 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.