Orthogonality of packings of paths and independent sets partitions on bipartite gr...
| Full text | |
| Author(s): |
Han, Jie
;
Zang, Chuanyun
;
Zhao, Yi
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF COMBINATORIAL THEORY SERIES A; v. 149, p. 115-147, JUL 2017. |
| Web of Science Citations: | 4 |
| Abstract | |
Given positive integers a <= b <= c, let K-a,K-b,K-c be the complete 3-partite 3-uniform hypergraph with three parts of sizes a,b,c. Let H be a 3-uniform hypergraph on n vertices where n is divisible by a+b+c. We asymptotically determine the minimum vertex degree of H that guarantees a perfect K-a,K-b,K-c-tiling, that is, a spanning subgraph of H consisting of vertex-disjoint copies of K-a,K-b,K-c. This partially answers a question of Mycroft, who proved an analogous result with respect to codegree for r-uniform hypergraphs for all r >= 3. Our proof uses a lattice-based absorbing method, the concept of fractional tiling, and a recent result on shadows for 3-graphs. (C) 2017 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 |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 15/07869-8 - Perfect matchings and Tilings in hypergraphs |
| Grantee: | Jie Han |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |