The minimum size of 3-graphs without a 4-set spanning no or exactly three edges
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 0195-6698Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.ejc.2011.03.006
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|
|Official Date:||October 2011|
|Page Range:||pp. 1142-1155|
|Access rights to Published version:||Restricted or Subscription Access|
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