Note on incidence chromatic number of subquartic graphs

An incidence in a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident to v. Two incidences (v, e) and (u, f) are adjacent if at least one of the following holds: ((a) v = u, (b) e = f), or ((c) vu in {e,f}). An incidence coloring of G is a coloring of its incidences assigning distinct colors to adjacent incidences. In this note we prove that every subquartic graph admits an incidence coloring with at most seven colors.