The coloring number of a graph G was defined by to be the least &kappa; for which there exists an ordering of the vertices of G in which each vertex has fewer than &kappa; neighbors that are earlier in the ordering.
A third, equivalent formulation is that G is k-degenerate (or has coloring number at most k + 1) if and only if the edges of G can be oriented to form a directed acyclic graph with outdegree at most k [REF].