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 -