A Turán theorem for extensions via an ErdősKoRado theorem for Lagrangians
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 $(r2)$ new vertices. In this paper we determine the Turán number of the extension of an $r$graph consisting of two vertexdisjoint edges, settling a conjecture of Hefetz and Keevash, who previously determined this Turán 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 $r \geq 4$.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 DOI:
 10.48550/arXiv.1707.01533
 arXiv:
 arXiv:1707.01533
 Bibcode:
 2017arXiv170701533B
 Keywords:

 Mathematics  Combinatorics