대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제53권1호
  • /
  • Pages.139-151
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  • 2016
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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TOTAL COLORINGS OF PLANAR GRAPHS WITH MAXIMUM DEGREE AT LEAST 7 AND WITHOUT ADJACENT 5-CYCLES

  • Tan, Xiang (School of Mathematics and Quantitative Economics Shandong University of Finance and Economics)
  • 투고 : 2015.01.05
  • 발행 : 2016.01.31
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⟨ 이전 논문 다음 논문 ⟩

초록

A k-total-coloring of a graph G is a coloring of $V{\cup}E$ using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number ${\chi}^{{\prime}{\prime}}(G)$ of G is the smallest integer k such that G has a k-total-coloring. Let G be a planar graph with maximum degree ${\Delta}$. In this paper, it's proved that if ${\Delta}{\geq}7$ and G does not contain adjacent 5-cycles, then the total chromatic number ${\chi}^{{\prime}{\prime}}(G)$ is ${\Delta}+1$.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

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