Adapted game colouring of graphs

摘要: Suppose G=(V,E) is a graph and F colouring of its edges (not necessarily proper) that uses the colour set X. In an adapted game, Alice Bob alternately uncoloured vertices G with colours from A partial c legal if there no edge e=xy such c(x)=c(y)=F(e). process each must be legal. If eventually all are coloured, then wins game. Otherwise, The game chromatic number G, denoted by @g"a"d"g(G), minimum needed to ensure for any has winning strategy This paper studies various classes graphs. We prove maximum trees 3, outerplanar graphs 5, k-trees at most 2k+1, planar 11.