Total colorings of planar graphs with maximum degree seven and without intersecting 3-cycles

Let GG be a planar graph with maximum degree Δ≥7Δ≥7 and without intersecting 3-cycles; that is, two cycles of length 3 are not incident with a common vertex. Then the total chromatic number of GG is Δ+1Δ+1.

► In this study, we investigate total colorings of planar graphs with maximum degree seven.
► We use the discharging method in the proofs.
► It is proved that, if a planar graph GG contains no intersecting triangles and Δ(G)≥7Δ(G)≥7, then χ″(G)=Δ+1χ″(G)=Δ+1.