A structural theorem for planar graphs with some applications |
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| Authors: | Huiyu ShengYingqian Wang |
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| Affiliation: | College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China |
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| Abstract: | In this note, we prove a structural theorem for planar graphs, namely that every planar graph has one of four possible configurations: (1) a vertex of degree 1, (2) intersecting triangles, (3) an edge xy with d(x)+d(y)≤9, (4) a 2-alternating cycle. Applying this theorem, new moderate results on edge choosability, total choosability, edge-partitions and linear arboricity of planar graphs are obtained. |
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| Keywords: | Planar graph Intersecting triangles List edge-coloring List total coloring Edge-partition Linear 2-arboricity |
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