A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable

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	A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable
其他题名	A Sufficient Condition for Planar Graphs with Maximum Degree 8 to Be 9-totally Colorable
	Cai Jian Sheng 1; Teng Chang Chun 1; Yan Gui Ying 2
	2014-01-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	30 期号:6 页码:993-1006
摘要	A total k-coloring of a graph G is a coloring of V (G) a(a) E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number chi aEuro(3)(G) is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree Delta a parts per thousand yen 9, then chi aEuro(3)(G) = Delta+1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then chi aEuro(3)(G) = 9.
其他摘要	A total k-coloring of a graph G is a coloring of V (G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ''(G) is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree Δ ≥ 9, then χ''(G) = Δ+1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then χ''(G) = 9.
关键词	TOTAL CHROMATIC NUMBER TOTAL COLORINGS Total coloring planar graph a fan of four adjacent 3-cycles
收录类别	CSCD
语种	英语
CSCD记录号	CSCD:5129732
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/54816
专题	中国科学院数学与系统科学研究院
作者单位	1.潍坊学院 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Cai Jian Sheng,Teng Chang Chun,Yan Gui Ying. A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2014,30(6):993-1006.
APA	Cai Jian Sheng,Teng Chang Chun,&Yan Gui Ying.(2014).A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable.ACTA MATHEMATICA SINICA-ENGLISH SERIES,30(6),993-1006.
MLA	Cai Jian Sheng,et al."A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable".ACTA MATHEMATICA SINICA-ENGLISH SERIES 30.6(2014):993-1006.