Note on Coloring the Square of an Outerplanar Graph

Abstract

A new proof is given to the following result of ours. Let \(G\) be an outerplanar graph with maximum degree \(\Delta \geq 3\). The chromatic number \(\chi(G^2)\) of the square of \(G\) is at most \(\Delta+2\), and \(\chi(G^2) = \Delta+1\) if \(\Delta \geq 7\).