A hypergraph Turan theorem via lagrangians of intersecting families

作者：Hefetz Dan^*; Keevash Peter

来源：Journal of Combinatorial Theory - Series A, 2013, 120(8): 2020-2038.

DOI：10.1016/j.jcta.2013.07.011

Let K-3,3(3) be the 3-graph with 15 vertices {x(i), y(i): 1 %26lt;= i %26lt;= 3} and (z(ij): 1 %26lt;= i, j %26lt;= 3}, and 11 edges {x(i), x(2), x(3)}, {y(2), y(2), y(3)} and {{x(i), y(j), z(ij)}: 1 %26lt;= i, j %26lt;= 3}. We show that for large n, the unique largest K-3,3(3)-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.

• 出版日期2013-11