neighbordistinguishingtotalchoicenumberofsparsegraphsviathecombinatorialnullstellensatz
文献类型：期刊论文
| 作者 | Qu Cunquan1; Ding Laihao1; Wang Guanghui1; Yan Guiying2
|
| 刊名 | actamathematicaeapplicataesinicaenglishseries
 |
| 出版日期 | 2016 |
| 卷号 | 32期号:2页码:537 |
| ISSN号 | 0168-9673 |
| 英文摘要 | 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 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/46075]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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