On the First-Fit Chromatic Number of Graphs

The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the maximum number of classes in an ordered partition of the vertex set of a graph G into independent sets V1, V2, . . . , Vk so that for each 1 i < j k and for each x Vj there exists a y Vi such that x and y are adjacent. In this paper, we study the first-fit chromatic number of outerplanar and planar graphs as well as Cartesian products of graphs, and in particular we give asymptotically tight results for outerplanar graphs. Key words. first-fit chromatic number, Grundy number, Grundy coloring, greedy coloring, random graph, planar graph, Cartesian product AMS subject classifications. 05C15, 05C35, 05C85 DOI. 10.1137/060672479

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: József Balogh, Stephen G. Hartke, Qi Liu, Gexin Yu
• Keywords: First-fit Chromatic Number, Grundy Number, Maximum Number, SIAMDM 2008