Kneser's conjecture and the octahedral Tucker lemma
A Lean 4 / Mathlib formalization of Lovász's theorem (Kneser's conjecture): for 0 < k and 2k ≤ n the Kneser graph KG(n, k) of k-subsets of an n-set, adjacent when disjoint, has chromatic number exactly n − 2k + 2; proved combinatorially from the octahedral Tucker lemma (an antipodal labelling of the nonzero sign vectors of length n by nonzero integers in [−m, m] with m < n has a complementary pair x ≼ y with λ(x) = −λ(y)), which is itself proved by Ky Fan's parity argument. Mathlib has neither Kneser graphs nor Tucker's lemma.
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