  Given a graph G and an integer k, two players take turns coloring the
vertices of G one by one using k colors so that neighboring vertices get
different colors. The first player wins iff at the end of the game all the
vertices of $G$ are colored. The game chromatic number \chi_g(G) is the minimum
k for which the first player has a winning strategy. The paper \cite{BFS} began
the analysis of the asymptotic behavior of this parameter for a random graph
G_{n,p}. This paper provides some further analysis for graphs with constant
average degree i.e. np=O(1) and for random regular graphs.
