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The Asymptotic Combinatorics of Permutations and Flag Algebras
| Full text | |
| Author(s): |
Han, Jie
Total Authors: 1
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON DISCRETE MATHEMATICS; v. 30, n. 3, p. 1453-1469, 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
Suppose k inverted iota n and H is an n-vertex k-uniform hypergraph. A near perfect matching in H is a matching of size left perpendicularn/kright perpendicular. We give a divisibility barrier construction that prevents the existence of near perfect matchings in H. This generalizes the divisibility barrier for perfect matchings. We give a conjecture on the minimum d-degree threshold forcing a (near) perfect matching in H which generalizes a well-known conjecture on perfect matchings. We also verify our conjecture for various cases. Our proof makes use of the lattice-based absorbing method that we used recently to solve two other problems on matching and tilings for hypergraphs. (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: | 15/07869-8 - Perfect matchings and Tilings in hypergraphs |
| Grantee: | Jie Han |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |