Total Colorings of Planar Graphs with Maximum Degree Seven and without 3-Cycles Adjacent to 4-Cycles

Let G be a planar graph with maximum degree ΔΔ¡Y7 and without 3-cycles adjacent to 4-cycles, that is, any 3-cycle has not a common edge with a 4-cycle. Then the total chromatic number of G is (ΔΔ+1).