Published November 9, 2026 | Version v1.0.1

R(12,12) ≥ 1661: a colouring of K_1660, a Lean proof and computer checks

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Description

A red/blue colouring of the complete graph on 1660 vertices with no monochromatic K_12, so R(12,12) ≥ 1661. It consists of the Mathon–Shearer colouring M(797) with 21 vertices removed, and 85 core vertices, each a copy of a removed vertex or constant on the rest of M(797). The removed vertices contain two antipodal pairs of M(797). Checked by two independent exhaustive computer searches and by a clone-projection argument with an antipodal rule, and proved in Lean 4 with Mathlib; the compiled proof was also accepted by leanchecker and by the independent kernel nanoda. The work was done with Claude (Claude Opus 5.5, Anthropic); see the README.

Notes

If you use this colouring, please cite it as below, together with Tatarevic's paper, r1212-1642 and r1212-1658.

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YueMa0/r1212-1661-v1.0.1.zip

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