Total coloring of planar graphs with maximum degree 8

Let G   be a planar graph with Δ⩾8Δ⩾8 and without adjacent cycles of size i and j  , for some 3⩽i⩽j⩽53⩽i⩽j⩽5. In this paper, it is proved that G   is (Δ+1)(Δ+1)-total-colorable.