Abstract :
In this note we show that the concept of incidence coloring introduced by Brualdi and Massey [4] is a special case of directed star arboricity, introduced by Agor and Alon [2]. A conjecture in [4] concerning asymptotics of the incidence coloring number is solved in the negative following an example in [2]. We generalize a result in [3] concerning the star arboricity of graphs to the directed case by a slight modification of their proof, to give the same asymptotic bound as in the undirected case. As a result, we get tight asymptotic bounds for the maximum incidence coloring number of a graph in terms of its degree.
