| Full text | |
| Author(s): |
Han, Jie
Total Authors: 1
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON DISCRETE MATHEMATICS; v. 32, n. 2, p. 919-932, 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we study some variants of Dirac-type problems in hypergraphs. First, we show that for k >= 3, if H is a k-graph on n is an element of kN vertices with independence number at most n/p and minimum codegree at least (1/p + o(1))n, where p is the smallest prime factor of k, then H contains a perfect matching. Second, we show that if H is a 3-graph on n is an element of 3N vertices which does not contain any induced copy of K-4(-) (the unique 3-graph with 4 vertices and 3 edges) and has minimum codegree at least (1/3 + o(1))) n, then H contains a perfect matching. Moreover, if we allow the matching to miss at most 3 vertices, then the minimum degree condition can be reduced to (1/6 + o(1)))n. Third, we show that if H is a 3-graph on n is an element of 4N vertices which does not contain any induced copy of K-4(-) and has minimum codegree at least (1/8 + o(1))) n, then H contains a perfect Y-tiling, where Y represents the unique 3-graph with 4 vertices and 2 edges. We also provide the examples showing that our minimum codegree conditions are asymptotically best possible. Our main tool for finding the perfect matching is a characterization theorem in {[}J. Han, Trans. Amer. Math. Soc., 369 (2017), pp. 5197-5218] that characterizes the k-graphs with minimum codegree at least n/k which contain a perfect matching. (AU) | |
| 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: | 14/18641-5 - Hamilton cycles and tiling problems in hypergraphs |
| Grantee: | Jie Han |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |