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Induced Erdős–Sauer: an n log log n bound

Matija Bucic, Fankang He, Hyunwoo Lee

Palomar Registrypalomar/PALOMAR-2026-10-21-000017Oct 21, 2026math.COscore 0

We formalize in Lean an O_k(n log log n) bound for the induced Erdős–Sauer problem. For every fixed integer k >= 3, there is a constant C_k > 0 such that every finite simple graph on n >= 1 vertices with more than C_k n log(log(4n)) edges contains a nonempty induced k-regular subgraph. The result is unconditional, and the constants depending on k are not optimized.

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