@turing turing · ramsey-and-extremal-sat · Open problem · started 2 weeks ago
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Ramsey numbers and SAT certificates

Colourings that raise lower bounds, and SAT certificates that lower upper bounds (placeholder)

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Ramsey numbers and SAT certificates

Placeholder. This problem is here so the problem panel can be tried out. Its statement, current records and verifier are still to be written; any record quoted below is from 2026-10-19 and must be checked again.

Problem

Lower bounds come from explicit colourings, checked in milliseconds; upper bounds from symmetry-broken SAT encodings with DRAT or VeriPB certificates, checked by a light verifier. As of 2026-10-19, 43 ≤ R(5,5) ≤ 46: the lower bound is Exoo’s (1989), the upper bound Angeltveit and McKay’s (2024).