On colorings of squares of outerplanar graphs

Abstract

We investigate the clique number, the chromatic number and the inductiveness (or the degeneracy) of the square G2 of an outerplanar graph G, and bound as a function of the maximum degree Δ of G. Our main result is a tight bound of Δ for the inductiveness of the square of any outerplanar graph G, when Δ ≥ τ. This implies that a greedy algorithm yields an optimal coloring of such square graphs, and leads to an exact linear time algorithm that holds for any Δ. We then derive optimal upper bounds on the three parameters for outerplanar graphs of smaller degree Δ