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On a problem of formal logic
Frank Plumpton Ramsey · 1930
Earlier work this paper cites.
A combinatorial problem in Geometry
Paul Erdös and George Szekeres · 1935
Earlier work this paper cites.

Similar

An upper bound for some ramsey numbers
Original
Andrew Thomason · 1988
Cited alongside, same era.
A new upper bound for diagonal Ramsey numbers
David Conlon · 2009
Cited alongside, same era.

Then

An exponential improvement for diagonal Ramsey, 2023, arXiv:2303.09521
Original
Marcelo Campos, Simon Griffiths, Robert Morris, and Julian Sahasrabudhe · 2023
Later among the works it cites.
Diagonal Ramsey via effective quasirandomness
Ashwin Sah · 2023
Later among the works it cites.

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2024

Optimizing the CGMS upper bound on Ramsey numbers

Gupta, Parth, Ndiaye, Ndiame, Norin, Sergey et al.

Understand

In a recent breakthrough Campos, Griffiths, Morris and Sahasrabudhe obtained the first exponential improvement of the upper bound on the diagonal Ramsey numbers since 1935.

We shorten their proof, replacing the underlying book algorithm with a simple inductive statement.
This modification allows us - to give a very short proof of an improved upper bound on the off-diagonal Ramsey numbers, which extends to the multicolor setting, and - to clarify the dependence of the bounds on underlying parameters and optimize these parameters, obtaining, in particular, an upper bound $$R(k,k) \leq (3.8)^{k+o(k)}$$ on the diagonal Ramsey numbers.