2017/07/05 by Adam Bene Watts, Sergey Norin, Watts, Adam Bene +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1707.01533
arxiv created 2017/07/05 · arxiv updated 2017/07/07
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.