The incidence coloring conjecture for graphs of maximum degree 3

The incidence coloring conjecture, or ICC, states that any graph can be incidence-colored with Δ+2 colors, where Δ is the maximum degree of the graph. After being introduced in 1993 by Brualdi and Massey, ICC was shown to be false in general by Guiduli in 1997, following the work of Algor and Alon. However, Shiu, Lam and Chen conjectured that the ICC holds for cubic graphs and proved it for some classes of such graphs. In this paper we prove the ICC for any graph with Δ=3.