Name
Abstract | ||
|---|---|---|
A Hamilton -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 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 n4k2, there is an n-vertex k-uniform hypergraph, with degree sum of any two strongly independent sets of k1 vertices bigger than 2n4(k1), contains no Hamilton l-cycle, 1k1. (ii) If the degree sum of two weakly independent sets of k1 vertices in an n-vertex k-uniform hypergraph is (1+o(1))n, then the hypergraph contains a Hamilton (k1)-cycle, where two distinct sets of k1 vertices are weakly (strongly) independent if there exist no edge containing the union of them (intersecting both of them). |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.disc.2017.02.018 | Discrete Mathematics |
Keywords | Field | DocType |
Cycle,Hamiltonian,Hypergraph,Ore-type | Graph center,Discrete mathematics,Combinatorics,Vertex (geometry),Hamiltonian path,Constraint graph,Hypergraph,Distance,Independent set,Mathematics,Path graph | Journal |
Volume | Issue | ISSN |
340 | 7 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yucong Tang | 1 | 0 | 0.34 |
| Guiying Yan | 2 | 196 | 22.92 |