Tutte's f-factor theorem
A Lean 4 / Mathlib formalization of Tutte's f-factor theorem: a finite simple graph G has a spanning subgraph H with deg_H v = f v for every vertex v if and only if, for all disjoint vertex sets S and T, q(S, T) ≤ ∑_{v ∈ S} f v − ∑_{v ∈ T} f v + ∑_{v ∈ T} deg_{G−S} v, where q(S, T) is the number of connected components C of G − (S ∪ T) for which ∑_{v ∈ C} f v + e(C, T) is odd and deg_{G−S} v is the number of neighbours of v outside S. Mathlib has Tutte's 1-factor theorem but not the f-factor theorem.
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