Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable |
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| Authors: | Dingzhu Du |
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| Institution: | College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang Jinhua 321004, China |
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| Abstract: | The Total Coloring Conjecture, in short, TCC, says that every simple graph is (Δ+2)-totally-colorable where Δ is the maximum degree of the graph. Even for planar graphs this conjecture has not been completely settled yet. However, every planar graph with Δ≥9 has been proved to be (Δ+1)-totally-colorable. In this paper, we prove that planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable. |
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| Keywords: | Planar graph Total coloring Maximum degree Adjacent triangles |
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