Some results on the incidence coloring number of a graph

This paper proves that if G is a cubic graph which has a Hamiltonian path or G is a bridgeless cubic graph of large girth, then its incidence coloring number is at most 5. By relating the incidence coloring number of a graph G to the chromatic number of G 2 , we present simple proofs of some known results, and characterize regular graphs G whose incidence coloring number equals Δ ( G ) + 1 .