Total colorings of planar graphs without adjacent triangles |
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| Authors: | Xiang-Yong Sun Jian-Liang Wu Yu-Wen Wu |
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| Institution: | a School of Mathematics, Shandong University, Jinan, 250100, China
b School of Statistics and Math., Shandong Economic University, Jinan, 250014, China |
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| Abstract: | Let G be a planar graph without adjacent 3-cycles, that is, two cycles of length 3 are not incident with a common edge. In this paper, it is proved that the total coloring conjecture is true for G; moreover, if Δ(G)≥9, then the total chromatic number χ″(G) of G is Δ(G)+1. Some other related results are obtained, too. |
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| Keywords: | Planar graph Total coloring Triangle |
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