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 An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs Tang, Yucong; Yan, Guiying1 2017-07-01 Source Publication DISCRETE MATHEMATICS ISSN 0012-365X Volume 340Issue:7Pages:1528-1534 Abstract 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. Keyword Cycle Hamiltonian Hypergraph Ore-type DOI 10.1016/j.disc.2017.02.018 Language 英语 WOS Research Area Mathematics WOS Subject Mathematics WOS ID WOS:000400221800011 Publisher ELSEVIER SCIENCE BV Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/25971 Collection 应用数学研究所 Corresponding Author Yan, Guiying Affiliation 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China Recommended CitationGB/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.
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