| Full text | |
| Author(s): |
Alvarado, Jose D.
;
Kohayakawa, Yoshiharu
;
Lang, Richard
;
Mota, Guilherme Oliveira
;
Stagni, Henrique
Total Authors: 5
|
| Document type: | Journal article |
| Source: | XII LATIN-AMERICAN ALGORITHMS, GRAPHS AND OPTIMIZATION SYMPOSIUM, LAGOS 2023; v. 224, p. 8-pg., 2023-01-01. |
| Abstract | |
We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum d-degree threshold for loose Hamiltonicity relative to the random k-uniform hypergraph H-k(n, p) coincides with its dense analogue whenever p >= n(-(k-1)/2+o(1)). The value of p is approximately tight for d > (k + 1)/2. This is particularly interesting because the dense threshold itself is not known beyond the cases when d >= k - 2. (C) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) (AU) | |
| FAPESP's process: | 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics |
| Grantee: | Guilherme Oliveira Mota |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 21/11020-9 - Large substructures in random graphs and hypergraphs |
| Grantee: | Yoshiharu Kohayakawa |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 19/13364-7 - Extremal and structural problems in graph theory |
| Grantee: | Cristina Gomes Fernandes |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 20/10796-0 - Structural problems in random graphs |
| Grantee: | José Diego Alvarado Morales |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |