论文信息 - A hypergraph Turán theorem via lagrangians of intersecting families

A hypergraph Turán theorem via lagrangians of intersecting families

Let \( K_{3,3}^3 \), be the 3-graph with 15 vertices {x i , y i :1 ≤ i ≤ 3} and {z ij :1 ≤ i, j ≤ 3}, and 11 edges {x 1 , x 2 , x 3 }. {y 1 , y 2 , y 3 } and {{x i , y j , z ij }: 1 ≤ i, j ≤ 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.

Peter Keevash | Dan Hefetz

[1] Vojtech Rödl,et al. Applications of the regularity lemma for uniform hypergraphs , 2006, Random Struct. Algorithms.

[3] Vojtech Rödl,et al. Hypergraphs do not jump , 1984, Comb..

[4] P. Erdös. On extremal problems of graphs and generalized graphs , 1964 .

[5] Chi-Kwong Li,et al. A research problem , 1996 .

[6] John M. Talbot. Lagrangians Of Hypergraphs , 2002, Comb. Probab. Comput..

[7] Dhruv Mubayi,et al. The Turán Number of F3, 3 , 2012, Comb. Probab. Comput..

[8] Zoltán Füredi,et al. An exact result for 3-graphs , 1984, Discret. Math..

[9] Peter Keevash. Surveys in Combinatorics 2011: Hypergraph Turán problems , 2011 .

[10] Oleg Pikhurko. An exact Turán result for the generalized triangle , 2008, Comb..

[11] P. Erdös,et al. INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS , 1961 .

[12] John M. Talbot,et al. New Turán Densities for 3-Graphs , 2012, Electron. J. Comb..

[13] Zoltán Füredi,et al. Extremal problems whose solutions are the blowups of the small witt-designs , 1989, J. Comb. Theory, Ser. A.

[14] Rudolf Ahlswede,et al. Search Problems , 1987 .

[15] Emil R. Vaughan,et al. On applications of Razborov's flag algebra calculus to extremal 3-graph theory , 2011, 1110.1623.