We investigate a competitive version of the coloring number of a graph G = (V, E). For a fixed linear ordering L of V let s (L) be one more than the maximum outdegree of G when G is oriented so that x ← y if x <
L
y. The coloring number of G is the minimum of s (L) over all such orderings. The (a, b)-marking game is played on a graph G = (...... hiện toàn bộ