#TITLE_ALTERNATIVE# - HAYATI, NORMA
Given a graph G and a set of colors {1, 2, ..., k}. Two players alternately color the vertices of G. The first player (A) is aiming that all vertices of G are colored, and the second player (B) is trying to prevent this. The only rule they must obey is to color a vertex with a color different from all the colors that appeare in its neighborhood (at the time of the coloring). If all the vertices of the graph are colored, A wins, otherwise B wins (that is, at a certain state of the game there appears an uncolored vertex whose neighborhood contains all colors). The smallest k such A has a winning strategy on G using k colors is called the game chromatic number of G.