On the maximum average degree and the incidence chromatic number of a graph

Abstract

We prove that the incidence chromatic number of every 3-degenerated graph G is at most Δ(G) + 4. It is known that the incidence chromatic number of every graph G with maximum average degree mad(G) < 3 is at most Δ(G) + 3. We show that when Δ(G) ≥ 5, this bound may be decreased to Δ(G) + 2. Moreover, we show that for every graph G with mad(G) < 22/9 (resp. with mad(G) < 16/7 and Δ(G) ≥ 4), this bound may be decreased to Δ(G) + 2 (resp. to Δ(G) + 1). © 2005 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.