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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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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
Volume: Vol.32
Number: No.7
Page Range: pp. 1142-1155
Identification Number: 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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