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neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz
Qu Cunquan1; Ding Laihao1; Wang Guanghui1; Yan Guiying2
2016
Source Publicationactamathematicaeapplicataesinicaenglishseries
ISSN0168-9673
Volume32Issue:2Pages:537
AbstractAbstract 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 .
Language英语
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/46076
Collection应用数学研究所
Affiliation1.山东大学
2.中国科学院数学与系统科学研究院
Recommended Citation
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.
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