A hypergraph Turán theorem via lagrangians of intersecting families

Dan Hefetz; Peter Keevash

doi:https://doi.org/10.1016/j.jcta.2013.07.011

A hypergraph Turán theorem via lagrangians of intersecting families

Dan Hefetz, Peter Keevash

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	2020-2038
Number of pages	19
Journal	Journal of Combinatorial Theory. Series A
Volume	120
Issue number	8
DOIs	https://doi.org/10.1016/j.jcta.2013.07.011
State	Published - Nov 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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Cite this

@article{ea135d670f40458f9aa77adcb6295ecc,

title = "A hypergraph Tur{\'a}n theorem via lagrangians of intersecting families",

abstract = "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.",

author = "Dan Hefetz and Peter Keevash",

note = "Funding Information: Research supported in part by ERC grant 239696 and EPSRC grant EP/G056730/1 .",

year = "2013",

month = nov,

doi = "https://doi.org/10.1016/j.jcta.2013.07.011",

language = "الإنجليزيّة",

volume = "120",

pages = "2020--2038",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "8",

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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.

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U2 - https://doi.org/10.1016/j.jcta.2013.07.011

DO - https://doi.org/10.1016/j.jcta.2013.07.011

M3 - مقالة

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 -

A hypergraph Turán theorem via lagrangians of intersecting families

Abstract

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