neighborsumdistinguishingtotalcoloringsviathecombinatorialnullstellensatz

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	neighborsumdistinguishingtotalcoloringsviathecombinatorialnullstellensatz
	Ding Laihao 1; Wang Guanghui 1; Yan Guiying2
	2014
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	57 期号:9 页码:1875
摘要	Let G = (V E) be a graph and i be a total coloring of G by using the color set {1,2,...,k} Let f(v) denote the sum of the color of the vertex v and the colors of all incident edges of v. We say that phi is neighbor sum distinguishing if for each edge uv is an element of E(G), f(u) not equal f(v). The smallest number k is called the neighbor sum distinguishing total chromatic number, denoted by chi(nsd)''(G). Pilsniak and Wozniak conjectured that for any graph G with at least two vertices, chi(nsd)''(G) <= Delta(G) + 3. In this paper, by using the famous Combinatorial Nullstellensatz, we show that chi(nsd)''(G) <= 2 Delta (G) + col(G) - 1, where col(G) is the coloring number of G. Moreover, we prove this assertion in its list version.
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]
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/37541
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. neighborsumdistinguishingtotalcoloringsviathecombinatorialnullstellensatz[J]. sciencechinamathematics,2014,57(9):1875.
APA	Ding Laihao,Wang Guanghui,&Yan Guiying.(2014).neighborsumdistinguishingtotalcoloringsviathecombinatorialnullstellensatz.sciencechinamathematics,57(9),1875.
MLA	Ding Laihao,et al."neighborsumdistinguishingtotalcoloringsviathecombinatorialnullstellensatz".sciencechinamathematics 57.9(2014):1875.