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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. doi:10.1016/j.ejc.2011.03.006 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) 946ā963] 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 nā„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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
DOI: | 10.1016/j.ejc.2011.03.006 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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