Abstract
Suppose that G is a planar graph with maximum degree Δ and without intersecting 4-cycles, that is, no two cycles of length 4 have a common vertex. Let χ ″ ( G ) , χ l ′ ( G ) and χ l ″ ( G ) denote the total chromatic number, list edge chromatic number and list total chromatic number of G , respectively. In this paper, it is proved that χ ″ ( G ) = Δ + 1 if Δ ≥ 7 , and χ l ′ ( G ) = Δ and χ l ″ ( G ) = Δ + 1 if Δ ( G ) ≥ 8 . Furthermore, if G is a graph embedded in a surface of nonnegative characteristic, then our results also hold.
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