Quasi-random hypergraphs and spanning subhypergraph containment
Advancements in Network Statistics: extensions to HPC and hypergraphs.
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Rhode Isl, Dept Math, 5 Lippitt Rd, Kingston, RI 02881 - USA
[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 - USA
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | JOURNAL OF COMBINATORIAL THEORY SERIES B; v. 144, p. 14-31, SEP 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
For integers k >= 3 and 1 <= l <= k - 1, we prove that for any alpha > 0, there exist epsilon > 0 and C > 0 such that for sufficiently large n is an element of (k - l)N, the union of a k-uniform hypergraph with minimum vertex degree alpha n(k-1) and a binomial random k-uniform hypergraph G((k)) (n, p) with p >= n(-(k-l)-epsilon) for l >= 2 and p >= Cn(-(k-1)) for l = 1 on the same vertex set contains a Hamiltonian l-cycle with high probability. Our result is best possible up to the values of epsilon and C and answers a question of Krivelevich, Kwan and Sudakov. (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 14/18641-5 - Hamilton cycles and tiling problems in hypergraphs |
| Grantee: | Jie Han |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |