TY - JOUR

T1 - A hypergraph Turán theorem via lagrangians of intersecting families

AU - Hefetz, Dan

AU - Keevash, Peter

N1 - Funding Information:
Research supported in part by ERC grant 239696 and EPSRC grant EP/G056730/1 .

PY - 2013/11

Y1 - 2013/11

N2 - Let K3,33 be the 3-graph with 15 vertices {x i, y i : 1 ≤ i ≤ 3} and {z i j : 1 ≤ i, j ≤ 3}, and 11 edges {x1, x2, x3}, {y1, y2, y3} and {{x i, y j, z i j} : 1 ≤ i, j ≤ 3}. We show that for large n, the unique largest K3,33-free 3-graph on n vertices is a balanced blow-up of the complete 3-graph on 5 vertices. Our proof uses the stability method and a result on lagrangians of intersecting families that has independent interest.

AB - Let K3,33 be the 3-graph with 15 vertices {x i, y i : 1 ≤ i ≤ 3} and {z i j : 1 ≤ i, j ≤ 3}, and 11 edges {x1, x2, x3}, {y1, y2, y3} and {{x i, y j, z i j} : 1 ≤ i, j ≤ 3}. We show that for large n, the unique largest K3,33-free 3-graph on n vertices is a balanced blow-up of the complete 3-graph on 5 vertices. Our proof uses the stability method and a result on lagrangians of intersecting families that has independent interest.

UR - http://www.scopus.com/inward/record.url?scp=84883338229&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2013.07.011

DO - 10.1016/j.jcta.2013.07.011

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AN - SCOPUS:84883338229

SN - 0097-3165

VL - 120

SP - 2020

EP - 2038

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 8

ER -