Circular Coloring of Planar Digraphs |
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Authors: | Guanghui Wang Bin Liu Jiguo Yu Guizhen Liu |
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Institution: | 1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China 2. School of Computer Science, Qufu Normal University, Rizhao, 276826, Shandong, China
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Abstract: | Let D be a digraph. The circular chromatic number ${\chi_c(D)}$ and chromatic number ${\chi(D)}$ of D were proposed recently by Bokal et?al. Let ${\vec{\chi_c}(G)={\rm max}\{\chi_c(D)| D\, {\rm is\, an\, orientation\, of} G\}}$ . Let G be a planar graph and n?≥ 2. We prove that if the girth of G is at least ${\frac{10n-5}{3},}$ then ${\vec{\chi_c}(G)\leq \frac{n}{n-1}}$ . We also study the circular chromatic number of some special planar digraphs. |
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