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The minimum size of 3-graphs without a 4-set spanning no or exactly three edges
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Pikhurko, Oleg. (2011) The minimum size of 3-graphs without a 4-set spanning no or exactly three edges. European Journal of Combinatorics, Vol.32 (No.7). pp. 1142-1155. ISSN 0195-6698
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Official URL: http://dx.doi.org/10.1016/j.ejc.2011.03.006
Abstract
Let Gi be the (unique) 3-graph with 4 vertices and i edges. Razborov [A. Razborov, On 3-hypergraphs with forbidden 4-vertex configurations, SIAM J. Discrete Math. 24 (2010) 946–963] determined asymptotically the minimum size of a 3-graph on n vertices having neither G0 nor G3 as an induced subgraph. Here we obtain the corresponding stability result, determine the extremal function exactly, and describe all extremal hypergraphs for n≥n0. It follows that any sequence of almost extremal hypergraphs converges, which answers in the affirmative a question posed by Razborov.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | European Journal of Combinatorics | ||||
| Publisher: | Academic Press | ||||
| ISSN: | 0195-6698 | ||||
| Official Date: | October 2011 | ||||
| Dates: |
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| Volume: | Vol.32 | ||||
| Number: | No.7 | ||||
| Page Range: | pp. 1142-1155 | ||||
| Identifier: | 10.1016/j.ejc.2011.03.006 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| URI: | http://wrap.warwick.ac.uk/id/eprint/43819 |
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