The Ramsey–Turán problem for cliques

Lüders, Clara Marie; Reiher, Christian

doi:10.1007/s11856-019-1831-4

Cited by 18 publications

(16 citation statements)

References 8 publications

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“…Capturing this more subtle behaviour, Fox, Loh and Zhao [13] proved that ̺(K 4 , δ) = 1 8 + Θ(δ). Building on Fox-Loh-Zhao's work, Lüders and Reiher [20] have very recently showed that, surprisingly, there is a precise Date: July 26, 2018. J.K. was supported by ERC grant 306349; Y.K.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Two Conjectures in Ramsey--Turán Theory

Kim¹,

Kim²,

Liu³

2019

SIAM J. Discrete Math.

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Section: Introduction and Resultsmentioning

confidence: 99%

Two Conjectures in Ramsey--Turán Theory

Kim¹,

Kim²,

Liu³

2019

SIAM J. Discrete Math.

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“…Thus Theorem 9 shows that C 2m+1 has a phase transition from n to o(n). Let us point out that RT(n, {C 3 , C 5 , C 7 }, s) s 2 appeared in [18] (Lemma 7.1).…”

Section: Denote By Kmentioning

confidence: 99%

“…It was motivated by the classical theorems of Ramsey and Turán and their connections to geometry, analysis, and number theory. Ramsey-Turán theory has attracted a great deal of attention over the last 40 years, see, e.g, [3,4,6,7,8,11,12,15,18,22,23], and a survey by Simonovits and Sós [20].…”

Section: Introductionmentioning

confidence: 99%

Two Results on Ramsey-Turán Theory

Li¹,

2021

Electron. J. Combin.

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“…[7,19]) and due to its applicability to other parts of extremal combinatorics, such as Turán's hypergraph problem and the Ramsey-Turán theory of graphs (see e.g. [5,13,14]).…”

Section: Fact 24 Let H Be a Hypergraph On 8 Vertices Not Containingmentioning

confidence: 99%

Turán’s Theorem for the Fano Plane

Bellmann

Reiher

2019

Combinatorica

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Confirming a conjecture of Vera T. Sós in a very strong sense, we give a complete solution to Turán's hypergraph problem for the Fano plane. That is we prove for n ě 8 that among all 3-uniform hypergraphs on n vertices not containing the Fano plane there is indeed exactly one whose number of edges is maximal, namely the balanced, complete, bipartite hypergraph. Moreover, for n " 7 there is exactly one other extremal configuration with the same number of edges: the hypergraph arising from a clique of order 7 by removing all five edges containing a fixed pair of vertices.For sufficiently large values n this was proved earlier by Füredi and Simonovits, and by Keevash and Sudakov, who utilised the stability method.2010 Mathematics Subject Classification. 05C65, 05D05.

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The Ramsey–Turán problem for cliques

Cited by 18 publications

References 8 publications

Two Conjectures in Ramsey--Turán Theory

Two Conjectures in Ramsey--Turán Theory

Two Results on Ramsey-Turán Theory

Turán’s Theorem for the Fano Plane

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