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- W3017382235 abstract "Since its formulation, Turan's hypergraph problems have been among the most challenging open problems in extremal combinatorics. One of them is the following: given a $3$-uniform hypergraph $mathcal{F}$ on $n$ vertices in which any five vertices span at least one edge, prove that $|mathcal{F}| ge (1/4 -o(1))binom{n}{3}$. The construction showing that this bound would be best possible is simply $binom{X}{3} cup binom{Y}{3}$ where $X$ and $Y$ evenly partition the vertex set. This construction has the following more general $(2p+1, p+1)$-property: any set of $2p+1$ vertices spans a complete sub-hypergraph on $p+1$ vertices. One of our main results says that, quite surprisingly, for all $p>2$ the $(2p+1,p+1)$-property implies the conjectured lower bound." @default.
- W3017382235 created "2020-04-24" @default.
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- W3017382235 date "2020-04-19" @default.
- W3017382235 modified "2023-10-17" @default.
- W3017382235 title "On local Tur'an problems" @default.
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