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Erdős Problem 809: rainbow odd cycles

Jacob Parish

Palomar Registrypalomar/PALOMAR-2026-09-30-000004Sep 30, 2026math.COscore 0

A Lean proof resolving the Burr–Erdős–Graham–Sós conjecture (Erdős Problem 809): for every fixed odd cycle of length at least seven, the maximal anti-Ramsey threshold at floor(n²/4) + 1 edges is n²/8 + o(n²). The seven-cycle case is new to our knowledge. The development proves it and formalizes the stronger full-density result of Bucić, Chen, and Ma for odd cycles of length at least nine.

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