Total colorings of planar graphs with small maximum degree

Let G be a planar graph of maximum degree ? and girth g, and there is an integer t(> g) such that G has no cycles of length from g+1 to t. Then the total chromatic number of G is ?+1 if (?,g,t) ? {(5,4,6), (4,4,17)}or ? = 3 and (g, t) ? {(5,13), (6,11), (7,11), (8,10), (9,10)}, where each vertex is incident with at most one g-cycle