The asymptotics of 𝑟(4,𝑡)

Sam Mattheus; Jacques Verstraete

doi:10.4007/annals.2024.199.2.8

The asymptotics of 𝑟(4,𝑡)

Sam Mattheus, Jacques Verstraete

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For integers s, t ≥ 2, the Ramsey number r(s, t) denotes the minimum n such that every n-vertex graph contains a clique of order s or an independent set of order t. In this paper we prove r(4, t) = (Formula presented.) as t → ∞, which determines r(4, t) up to a factor of order log² t, and solves a conjecture of Erdős.

Originele taal-2	English
Pagina's (van-tot)	919-941
Aantal pagina's	23
Tijdschrift	Annals of Mathematics
Volume	199
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.4007/annals.2024.199.2.8
Status	Published - 5 mrt 2024

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© 2024 Department of Mathematics, Princeton University.

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10.4007/annals.2024.199.2.8

Mattheus_Verstraete_with_adjustmentAccepted author manuscript, 338 KBLicentie: Unspecified

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The asymptotics of 𝑟(4,𝑡)

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