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Perfect matchings and K 4 3 -Tilings in hypergraphs of large codegree
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Pikhurko, Oleg (2008) Perfect matchings and K 4 3 -Tilings in hypergraphs of large codegree. Graphs and Combinatorics, Vol.24 (No.4). pp. 391-404. doi:10.1007/s00373-008-0787-7
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Official URL: http://dx.doi.org/10.1007/s00373-008-0787-7
Abstract
For a k-graph F, let t l (n, m, F) be the smallest integer t such that every k-graph G on n vertices in which every l-set of vertices is included in at least t edges contains a collection of vertex-disjoint F-subgraphs covering all but at most m vertices of G. Let K m k denote the complete k-graph on m vertices.
The function tk−1(kn0Kkk) (i.e. when we want to guarantee a perfect matching) has been previously determined by Kühn and Osthus [9] (asymptotically) and by Rödl, Ruciński, and Szemerédi [13] (exactly). Here we obtain asymptotic formulae for some other l. Namely, we prove that for any k4 and k2lk−2 ,
tl(kn0Kkk)=21+o(1)knk−l
.
Also, we present various bounds in another special but interesting case: t 2(n, m, K 43) with m = 0 or m = o(n), that is, when we want to tile (almost) all vertices by copies of K 43, the complete 3-graph on 4 vertices.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Graphs and Combinatorics | ||||
| Publisher: | Springer Japan KK | ||||
| ISSN: | 0911-0119 | ||||
| Official Date: | 2008 | ||||
| Dates: |
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| Volume: | Vol.24 | ||||
| Number: | No.4 | ||||
| Number of Pages: | 14 | ||||
| Page Range: | pp. 391-404 | ||||
| DOI: | 10.1007/s00373-008-0787-7 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | National Science Foundation (NSF) | ||||
| Grant number: | DMS-0457512 |
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