A new upper bound for total colourings of graphs Original Research Article

We give a new upper bound on the total chromatic number of a graph. This bound improves the results known for some classes of graphs. The bound is stated as follows: χT ⩽ χe + ⌊13χ⌋ + 2, where χ is the chromatic number, χe is the edge chromatic number (chromatic index) and χT is the total chromatic number.