The Classfication of B-perfect Graphs

This type of game was introduced by Bodlaender [2]. He considers a variant, which we will call game g, in which Alice must move first and passing is not allowed. In order to obtain upper and lower bounds for a parameter associated with game g, two other variants are useful. In the game B Bob may move first. He may also miss one or several turns, but Alice must always move. In the other variant, game A, Alice may move first and miss one or several turns, but Bob must move. So in game B Bob has some advantages, whereas in game A Alice has some advantages with respect to Bodlaender’s game.