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On the maximal number of edges in a homogeneous hypergraph not containing prohibited subgraphs. (English. Russian original) Zbl 0677.05064
Math. Notes 41, 247-259 (1987); translation from Mat. Zametki 41, No. 3, 433-455 (1987).
The author proves that the maximal number of edges of a 4-uniform hypergraph with n vertices without two edges whose symmetric difference is contained in a third is equal to $$\lfloor n/4\rfloor \lfloor (n+1)/4\rfloor \lfloor (n+2)/4\rfloor \lfloor (n+3)/4\rfloor$$ and that the extremal hypergraph is unique up to isomorphism. This settles a conjecture of B. Bollobás, who solved the corresponding problem for 3-uniform hypergraphs [Discrete Math. 8, 21-24 (1974; Zbl 0291.05114)].

##### MSC:
 05C65 Hypergraphs 05C35 Extremal problems in graph theory
##### Keywords:
maximal number of edges; extremal hypergraph
Full Text:
##### References:
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