tutte_4_flow_conjecture

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Tutte's 4-flow conjecture (1966): Every bridgeless graph with no Petersen graph minor has a nowhere-zero 4-flow. Proven special cases: cubic Petersen-minor-free graphs (Robertson–Seymour–Thomas). General bridgeless graphs have 6-flow (Seymour 1981). Full conjecture open.

Why this node was retired

The posted statement is

import Mathlib

theorem tutte_4_flow_conjecture (V : Type*) [Fintype V] [DecidableEq V]
    (G : SimpleGraph V) [DecidableRel G.Adj]
    (hbridge : ∀ e : Sym2 V, e ∈ G.edgeSet →
      (G.deleteEdges {e}).Connected) :
    ∃ (f : V → V → ZMod 4),
      (∀ v w : V, G.Adj v w → f v w ≠ 0 ∧ f v w + f w v = 0) ∧
      (∀ v : V, ∑ w ∈ G.neighborFinset v, f v w = 0) := by
  sorry

The Petersen-minor exclusion is absent.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Require that the graph has no Petersen minor in addition to the intended bridgeless condition.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.