A Turán Theorem for Extensions Via an Erdős-Ko-Rado 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 (r−2) new vertices. In this paper we determine the Turán 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 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≥4.

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Acknowledgement

Some of this research was performed in Summer 2015, when the first author was an undergraduate student at McGill University supported by an NSERC USRA scholarship.

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Correspondence to Liana Yepremyan.

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Watts, A.B., Norin, S. & Yepremyan, L. A Turán Theorem for Extensions Via an Erdős-Ko-Rado Theorem for Lagrangians. Combinatorica 39, 1149–1171 (2019). https://doi.org/10.1007/s00493-019-3831-8

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Mathematics Subject Classification (2010)

  • 05C35
  • 05C65
  • 05D05
  • 04D40