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Ruszinko Miklos (Renyi Intezet): Uniform hypergraphs containing neither grids nor triangles |
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Friday, 4. March 2016, 10:30 - 12:30
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| Abstract. A family of $r$-element sets ${A_1,...,A_r, B_1,...,B_r}$ forms a grid if $A_i\cap A_j=\emptyset$, $B_i\cap B_j=\emptyset$, $| A_i\cap B_j|=1$. A triangle is a collection of three of $r$-element sets which pairwise intersect in single and different points. The maximum size of linear $r$-hypergraphs containing neither grids nor triangles will be investigated. Tight bounds are obtained by generalizing Behrends construction on large sets of integers containing no long arithmetic progressions. Our results are related to the famous Ruzsa-Szemerédi theorem. This is a joint work with Zoltán Füredi. |
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Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged |
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