Abstract
A total k-coloring of a graph G is a coloring of V(G)∪E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ′′(G) of G is the smallest integer k such that G has a total k-coloring. In the paper, it is proved that for any K5-minor-free graph G, χ′′(G)≤Δ(G)+2 if Δ(G)≥7. Moreover, χ′′(G)=Δ(G)+1 if Δ(G)≥10.
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