| Texto completo | |
| Autor(es): |
Gao, Wei
;
Han, Jie
;
Zhao, Yi
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | COMBINATORICS PROBABILITY & COMPUTING; v. 28, n. 6, p. 31-pg., 2019-11-01. |
| Resumo | |
Given two k-graphs (k-uniform hypergraphs) F and H, a perfect F-tiling (or F-factor) in H is a set of vertex-disjoint copies of F that together cover the vertex set of H. For all complete k-partite k-graphs K, Mycroft proved a minimum codegree condition that guarantees a K-factor in an n-vertex k-graph, which is tight up to an error term o(n). In this paper we improve the error term in Mycroft's result to a sublinear term that relates to the Turan number of K when the differences of the sizes of the vertex classes of K are co-prime. Furthermore, we find a construction which shows that our improved codegree condition is asymptotically tight in infinitely many cases, thus disproving a conjecture of Mycroft. Finally, we determine exact minimum codegree conditions for tiling K-(k)(1, . . . , 1, 2) and tiling loose cycles, thus generalizing the results of Czygrinow, DeBiasio and Nagle, and of Czygrinow, respectively. (AU) | |
| Processo FAPESP: | 14/18641-5 - Circuitos hamiltonianos e problemas de ladrilhamento em hipergrafos |
| Beneficiário: | Jie Han |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 13/03447-6 - Estruturas combinatórias, otimização e algoritmos em Teoria da Computação |
| Beneficiário: | Carlos Eduardo Ferreira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 15/07869-8 - Emparelhamento perfeitos e ladrilhamentos em hipergrafos |
| Beneficiário: | Jie Han |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado |