Total colorings of planar graphs without adjacent triangles

Let G be a planar graph without adjacent 3-cycles, that is, two cycles of length 3 are not incident with a common edge. In this paper, it is proved that the total coloring conjecture is true for G ; moreover, if Δ ( G ) ≥ 9 , then the total chromatic number χ ″ ( G ) of G is Δ ( G ) + 1 . Some other related results are obtained, too.