Total Coloring of Planar Graphs Without Some Chordal 6-cycles

A k-total-coloring of a graph G is a coloring of vertex set and edge set using k colors such that no two adjacent or incident elements receive the same color. In this paper, we prove that if G is a planar graph with maximum Delta >= 8 and every 6-cycle of G contains at most one chord or any chordal 6-cycles are not adjacent, then G has a ( Delta + 1)-total-coloring.