On the First-Fit Chromatic Number of Graphs
József Balogh, Stephen G. Hartke, Qi Liu, Gexin Yu · SIAM Journal on Discrete Mathematics · 2008
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 $V_1, V_2, \dots, V_k$ so that for each $1\le i