Asymmetric graph coloring games

We introduce the (a; b)-coloring game, an asymmetric version of the coloring game played by two players Alice and Bob on a finite graph, which differs from the standard version in that, in each turn, Alice colors a vertices and Bob colors b vertices. We also introduce a related game, the (a; b)-marking game. We analyze these games and determine the (a; b)chromatic numbers and (a;b)-coloring numbers for the class of forests and all values of a and b. 2005 Wiley Periodicals, Inc. J Graph Theory 48: 169–185, 2005