Total colorings of planar graphs without chordal 6-cycles

摘要

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 of G is the smallest integer k such that G has a total k-coloring. In this paper, it is proved that if G is a planar graph with maximum degree Δ ≥ 7 and without chordal 6-cycles, then the total chromatic number of G is Δ + 1.