An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs
文献类型：期刊论文
| 作者 | Tang, Yucong; Yan, Guiying1
|
| 刊名 | DISCRETE MATHEMATICS
 |
| 出版日期 | 2017-07-01 |
| 卷号 | 340期号:7页码:1528-1534 |
| 关键词 | Cycle Hamiltonian Hypergraph Ore-type |
| ISSN号 | 0012-365X |
| DOI | 10.1016/j.disc.2017.02.018 |
| 英文摘要 | A Hamilton l-cycle in a k-uniform hypergraph of n-vertex is an ordering of all vertices, combined with an ordered subset.C of edges, such that any two consecutive edges share exactly l vertices and each edge in C contains k consecutive vertices. A classic result of O. Ore in 1960 is that if the degree sum of any two independent vertices in an n-vertex graph is at least n, then the graph contains a Hamiltonian cycle. Naturally, we consider to generalize it to hypergraphs situation. In this paper, we prove the following theorems. (i) For any n >= 4k(2), there is an n-vertex k-uniform hypergraph, with degree sum of any two strongly independent sets of k - 1 vertices bigger than 2n-4(k - I), contains no Hamilton l-cycle, 1 <= l <= k 1. (ii) If the degree sum of two weakly independent sets of k - 1 vertices in an n-vertex k-uniform hypergraph is (1 + o(1))n, then the hypergraph contains a Hamilton (k - 1)-cycle, where two distinct sets of k - 1 vertices are weakly (strongly) independent if there exist no edge containing the union of them (intersecting both of them). (C) 2017 Published by Elsevier B.V. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000400221800011 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/25970]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Yan, Guiying |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tang, Yucong,Yan, Guiying. An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs[J]. DISCRETE MATHEMATICS,2017,340(7):1528-1534. |
| APA | Tang, Yucong,&Yan, Guiying.(2017).An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs.DISCRETE MATHEMATICS,340(7),1528-1534. |
| MLA | Tang, Yucong,et al."An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs".DISCRETE MATHEMATICS 340.7(2017):1528-1534. |
入库方式： OAI收割
来源：数学与系统科学研究院
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