Star coloring outerplanar bipartite graphs

Abstract

In this thesis, we investigate a coloring problem on a special class of graphs. A proper coloring of a graph is a coloring of the vertices of the graph so that vertices joined by an edge get different colors. A star-coloring of a graph is a proper coloring of a graph with the additional constraint that there are no 2-colored paths on four vertices. A graph is said to be k-star-colorable if it can be star-colored with no more than k colors. It is well known that all outerplanar graphs are 6-star-colorable. We prove that all outerplanar bipartite graphs are 5-star-colorable and that there is a family of graphs that requires five colors. Keywords: graphs, star-coloring, planar, outerplanar, bipartite