Total Coloring With $\Delta + \mbox\lowercasepoly(\log \Delta)$ Colors

Authors:
Hugh Hind;Michael Molloy;Bruce Reed
Affiliations:
-;-;-
Venue:
SIAM Journal on Computing
Year:
1999

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Abstract

We provide a polynomial time algorithm which finds a total coloring of any graph with maximum degree $\D$, $\D$ sufficiently large, using at most $\D+8\log^8\D$ colors. This improves the best previous upper bound on the total chromatic number of $\D+18\D^{1/3}\log(3\D)$.