Vertex coloring the square of outerplanar graphs of low degree

Abstract

Vertex colorings of the square of an outerplanar graph have received a lot of attention recently. In this article we prove that the chromatic number of the square of an outerplanar graph of maximum degree = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree 6 6 is known. Hence, this mentioned chromatic number of 7 is the last and only unknown upper bound of the chromatic number in terms of .