We prove that the total chromatic number of any graph with maximum degree Δ is at most Δ plus an absolute constant. In particular, we show that for Δ sufficiently large, the total chromatic number of such a graph is at most Δ + 1026. The proof is probabilistic.
CITATION STYLE
Molloy, M., & Reed, B. (1998). A bound on the total chromatic number. Combinatorica, 18(2), 241–280. https://doi.org/10.1007/PL00009820
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