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List total colorings of planar graphs without triangles at small distance |
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| Authors: | |
| Institution: | [1]Department of Mathematics, Ocean University of China, Qingdao 266100, P. R. China [2]Center for Discrete Mathematics, Fuzhou University, Fuzhou 350002, P. R. China [3]School of Mathematics, Shandong University, Ji＇nan 250100, P. R. China |
| Abstract: | Suppose that G is a planar graph with maximum degree Δ. In this paper it is proved that G is total-(Δ + 2)-choosable if (1) Δ ≥ 7 and G has no adjacent triangles (i.e., no two triangles are incident with a common edge); or (2) Δ ≥ 6 and G has no intersecting triangles (i.e., no two triangles are incident with a common vertex); or (3) Δ ≥ 5, G has no adjacent triangles and G has no k-cycles for some integer k ∈ {5, 6}. |
| Keywords: | List total coloring choosability planar graph |
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