ENTIRE CHROMATIC NUMBER AND Δ-MATCHING OF OUTERPLANE GRAPHS

Let G be an outerplane graph with maximum degree Δ and the entire chromatic number χvef (G). This paper proves that if Δ ≥ 6, then Δ + 1 ≤ χvef (G) ≤ Δ + 2, and χvef (G) = Δ + 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.