Total colorings of planar graphs without adjacent triangles

Let GG 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 GG; moreover, if Δ(G)≥9Δ(G)≥9, then the total chromatic number χ″(G)χ″(G) of GG is Δ(G)+1Δ(G)+1. Some other related results are obtained, too.