On the First-Fit Chromatic Number of Graphs

  • Authors:

  • József Balogh;Stephen G. Hartke;Qi Liu;Gexin Yu

  • Affiliations:

  • jobal@math.uiuc.edu and qiliu@math.uiuc.edu;shartke2@math.unl.edu;-;gexin.yu@vanderbilt.edu

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2008

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Abstract

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