neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz

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	neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz
	Qu Cunquan 1; Ding Laihao 1; Wang Guanghui 1; Yan Guiying2
	2016
发表期刊	actamathematicaeapplicataesinicaenglishseries
ISSN	0168-9673
卷号	32 期号:2 页码:537
摘要	Abstract Let G = ( V,E ) be a graph and ? : V ∪ E → {1, 2, · · ·, k } be a total- k -coloring of G . Let f ( v )( S ( v )) denote the sum(set) of the color of vertex v and the colors of the edges incident with v . The total coloring ? is called neighbor sum distinguishing if ( f ( u ) ≠ f ( v )) for each edge uv ∈ E ( G ). We say that ? is neighbor set distinguishing or adjacent vertex distinguishing if S ( u ) ≠ S ( v ) for each edge uv ∈ E ( G ). For both problems, we have conjectures that such colorings exist for any graph G if k ≥ Δ( G ) + 3. The maximum average degree of G is the maximum of the average degree of its non-empty subgraphs, which is denoted by mad ( G ). In this paper, by using the Combinatorial Nullstellensatz and the discharging method, we prove that these two conjectures hold for sparse graphs in their list versions. More precisely, we prove that every graph G with maximum degree Δ( G ) and maximum average degree mad( G ) has ch Σ ″ ( G ) ≤ Δ( G ) + 3 (where ch Σ ″ ( G ) is the neighbor sum distinguishing total choice number of G ) if there exists a pair $$(k,m) in { (6,4),(5, tfrac{{18}}{5}),(4, tfrac{{16}}{5}) }$$ such that Δ( G ) ≥ k and mad ( G ) < m .
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/46076
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	Qu Cunquan,Ding Laihao,Wang Guanghui,et al. neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz[J]. actamathematicaeapplicataesinicaenglishseries,2016,32(2):537.
APA	Qu Cunquan,Ding Laihao,Wang Guanghui,&Yan Guiying.(2016).neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz.actamathematicaeapplicataesinicaenglishseries,32(2),537.
MLA	Qu Cunquan,et al."neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz".actamathematicaeapplicataesinicaenglishseries 32.2(2016):537.