Some results on the incidence coloring number of a graph

This paper proves that if GG is a cubic graph which has a Hamiltonian path or GG 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 GG to the chromatic number of G2G2, we present simple proofs of some known results, and characterize regular graphs GG whose incidence coloring number equals Δ(G)+1Δ(G)+1.