Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz

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	Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz
其他题名	Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz
	Ding LaiHao 1; Wang GuangHui 1; Yan GuiYing2
	2014
发表期刊	Science China Mathematics,
卷号	57 期号:9 页码:1875-1882
其他摘要	Abstract(#br)Let G = ( V,E ) be a graph and φ be a total coloring of G by using the color set {1, 2, ..., k }. Let f ( ν ) denote the sum of the color of the vertex ν and the colors of all incident edges of ν . We say that φ is neighbor sum distinguishing if for each edge uν ∈ E ( G ), f ( u ) ≠ f ( ν ). The smallest number k is called the neighbor sum distinguishing total chromatic number, denoted by χ nsd ″( G ). Pil?niak and Wo?niak conjectured that for any graph G with at least two vertices, χ nsd ″( G ) ? Δ( G ) + 3. In this paper, by using the famous Combinatorial Nullstellensatz, we show that χ nsd ″( G ) ? 2Δ( G )+col( G )?1, where col( G ) is the coloring number of G . Moreover, we prove this assertion in its list version.
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China] ; [Research Fund for the Doctoral Program of higher Education of China] ; [Scientific Research Foundation for the Excellent Middle Aged and Youth Scientists of Shandong Province of China]
CSCD记录号	CSCD:5217645
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/56327
专题	应用数学研究所
作者单位	1.山东大学 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	Ding LaiHao,Wang GuangHui,Yan GuiYing. Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz[J]. Science China Mathematics,,2014,57(9):1875-1882.
APA	Ding LaiHao,Wang GuangHui,&Yan GuiYing.(2014).Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz.Science China Mathematics,,57(9),1875-1882.
MLA	Ding LaiHao,et al."Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz".Science China Mathematics, 57.9(2014):1875-1882.