Edge-choosability of planar graphs without adjacent triangles or without 7-cycles |
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Authors: | Jianfeng Hou Jiansheng Cai |
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Affiliation: | School of Mathematics and System Sciences, Shandong University, Jinan, 250100, PR China |
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Abstract: | A graph G is edge-L-colorable, if for a given edge assignment L={L(e):e∈E(G)}, there exists a proper edge-coloring ? of G such that ?(e)∈L(e) for all e∈E(G). If G is edge-L-colorable for every edge assignment L with |L(e)|≥k for e∈E(G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph with maximum degree Δ(G)≠5 and without adjacent 3-cycles, or with maximum degree Δ(G)≠5,6 and without 7-cycles, then G is edge-(Δ(G)+1)-choosable. |
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Keywords: | Planar graph Edge-coloring Choosability Triangle Cycle |
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