{"id":"palomar/PALOMAR-2026-10-18-000005","url":"https://github.com/jtraverso/tutte-f-factor/tree/dc3bbce463c80c499d3e9fa072d13f9145d907d0","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-18-000005-v1.json","repo":"https://github.com/jtraverso/tutte-f-factor","tags":["math.CO","msc:05C70","msc:05C07","graph-theory","f-factors","lean","tutte-theorem"],"score":0,"title":"Tutte's f-factor theorem","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-18","reactions":{},"formalized":true,"formalizes":[{"title":"The Factors of Graphs","identifier":"doi:10.4153/CJM-1952-028-2","relationship":"formalizes"},{"title":"A Short Proof of the Factor Theorem for Finite Graphs","identifier":"doi:10.4153/CJM-1954-033-3","relationship":"formalizes"}]}