An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs

doi:10.1016/j.disc.2017.02.018

CSpace > 应用数学研究所

	An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs
	Tang, Yucong ; Yan, Guiying1
	2017-07-01
发表期刊	DISCRETE MATHEMATICS
ISSN	0012-365X
卷号	340 期号:7 页码:1528-1534
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.
关键词	Cycle Hamiltonian Hypergraph Ore-type
DOI	10.1016/j.disc.2017.02.018
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000400221800011
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25971
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.