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Near-linear cycles in connected vertex-transitive graphs

Matija Bucic

Palomar Registrypalomar/PALOMAR-2026-09-30-000015Sep 30, 2026math.COscore 0

A Lean formalization of the near-linear cycle theorem in "Lovász conjecture holds asymptotically". For every positive ε, sufficiently large connected finite vertex-transitive graphs contain a simple cycle with at least n^(1−ε) edges. The development includes a weaker-constant Bondy–Locke path-to-cycle comparison and the finite approximate-group and expansion arguments used in the path proofs.

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