Asymmetric marking games on line graphs

This paper investigates the asymmetric marking games on line graphs. Suppose G   is a graph with maximum degree ΔΔ and G has an orientation with maximum outdegree k  , we show that the (a,1)(a,1)-game coloring number of the line graph of G   is at most Δ+2k+⌈ka⌉-1. When a=1a=1, this improves some known results of the game coloring number of the line graphs.