The minimum size of 3-graphs without a 4-set spanning no or exactly three edges

Authors:
Oleg Pikhurko
Affiliations:
-
Venue:
European Journal of Combinatorics
Year:
2011

Citing 12
Cited 0

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Abstract

Let G"i 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 G"0 nor G"3 as an induced subgraph. Here we obtain the corresponding stability result, determine the extremal function exactly, and describe all extremal hypergraphs for n=n"0. It follows that any sequence of almost extremal hypergraphs converges, which answers in the affirmative a question posed by Razborov.