A Bound on the Total Chromatic Number

We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. In particular, we show that for su ciently large, the total chromatic number of such a graph is at most + 1026. The proof is probabilistic.

• Type: Journal
• Year: 1998
• Where: COMBINATORICA
• Authors: Michael Molloy, Bruce A. Reed
• Keywords: Absolute Constant, COMBINATORICA 1998, Maximum Degree, Total Chromatic Number