Total colorings of planar graphs without intersecting 4-cycles and intersecting 5-cycles - Tan, Xiang; Chen, Hong-Yu (Utilitas Mathematica, 2017)
Let G be a planar graph with maximum degree Δ. It is proved that if Δ ≥ 6 and G does not contain intersecting 4-cycles and intersecting 5-cycles, then the total chromatic number is Δ+1.