What question did this study set out to answer?

To verify the fixed r = 5 case of Erdős Problem 617 using machine proof assistants.

July 26, 2026Open Access

Machine verification of the fixed r = 5 case of Erdős Problem 617

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Independent verification of the Erdős–Gyárfás conjecture on five-colouring led to a verified mathematical result.

To verify the fixed r = 5 case of Erdős Problem 617 using machine proof assistants.
Used Lean 4 for formal verification of the five-colouring theorem.
Generated and verified 89 RUP-only LRAT certificates with independent checkers.
Provided a full audit trail with a reproducible verification process.
Confirmed the existence of a six-vertex set where one colour is absent with K₂₂₆.
Established the Ramsey identity R(6;5,4) = 26.

Ramazan Kara (2026) studied this question.

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