Total coloring of planar graphs with 7-cycles containing at most two chords

A k-total-coloring of a graph G is a coloring of vertices and edges of G 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 degree at least 8 and if every 7-cycle of G contains at most two chords, then G   has a (Δ+1)(Δ+1)-total-coloring.