Efficient Vertex- and Edge-Coloring of Outerplanar Graphs

Abstract

The problems of finding values of the chromatic number and the chromatic index of a graph are NP-hard even for some restricted classes of graphs. Every outerplanar graph has an associated tree structure which facilitates algorithmic treatment. Using that structure, we give an efficient algorithm to color the vertices of an outerplanar graph with the minimum number of colors. We also establish algorithmically the value of the chromatic index of an outerplanar graph. Our algorithms are based on systematic coloring of elements (vertices and edges, respectively) of adjacent faces.