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arXiv · 1707.01533

A Tur\'an theorem for extensions via an Erd\H{o}s-Ko-Rado theorem for Lagrangians

Adam Bene Watts·Sergey Norin·Liana Yepremyan
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Abstract

The extension of an $r$-uniform hypergraph $G$ is obtained from it by adding for every pair of vertices of $G$, which is not covered by an edge in $G$, an extra edge containing this pair and $(r-2)$ new vertices. In this paper we determine the Tur\'an number of the extension of an $r$-graph consisting of two vertex-disjoint edges, settling a conjecture of Hefetz and Keevash, who previously determined this Tur\'an number for $r=3$. As the key ingredient of the proof we show that the Lagrangian of intersecting $r$-graphs is maximized by principally intersecting $r$-graphs for $r \geq 4$.

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Adam Bene Watts, Sergey Norin, Liana Yepremyan. 2017-07-05. A Tur\'an theorem for extensions via an Erd\H{o}s-Ko-Rado theorem for Lagrangians. https://arxiv.org/abs/1707.01533

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