On the size-Ramsey number of grids

Conlon, David; Nenadov, Rajko; Trujić, Miloš

doi:10.48550/arxiv.2202.01654

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2022

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Cited by 2 publications

(2 citation statements)

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“…Clemens, Miralaei, Reding, Schacht and Taraz [5] gave an upper bound for the size Ramsey number of the 𝑡 × 𝑡 grid. Their bound was improved very recently by Conlon, Nenadov and Trujić [6]. Kim, Lee and Lee [17] proved Sidorenko's conjecture for grids (in arbitrary dimension).…”

Section: Introductionmentioning

confidence: 97%

The Turán number of the grid

Domagoj

Janzer

Sudakov

et al. 2022

Bulletin of London Math Soc

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For a positive integer 𝑡, let 𝐹 𝑡 denote the graph of the 𝑡 × 𝑡 grid. Motivated by a 50-year-old conjecture of Erdős about Turán numbers of 𝑟-degenerate graphs, we prove that there exists a constant 𝐶 = 𝐶(𝑡) such that ex(𝑛, 𝐹 𝑡 ) ⩽ 𝐶𝑛 3∕2 . This bound is tight up to the value of 𝐶. One of the interesting ingredients of our proof is a novel way of using the tensor power trick.

show abstract

Section: Introductionmentioning

confidence: 97%

The Turán number of the grid

Domagoj

Janzer

Sudakov

et al. 2022

Bulletin of London Math Soc

View full text Add to dashboard Cite

show abstract

“…Clemens, Miralaei, Reding, Schacht and Taraz [5] gave an upper bound for the size Ramsey number of the n × n grid. Their bound was improved very recently by Conlon, Nenadov and Trujić [6]. Kim, Lee and Lee [17] proved Sidorenko's conjecture for grids (in arbitrary dimension).…”

Section: Introductionmentioning

confidence: 97%