cycle_double_cover_conjecture

⚠️ Retired — specification defect

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

The cycle double cover conjecture (Szekeres 1973, Seymour 1979): Every 2-edge-connected graph has a cycle double cover, i.e., a multiset of cycles such that every edge appears in exactly two cycles of the collection.

Why this node was retired

The posted statement is

import Mathlib

theorem cycle_double_cover_conjecture (V : Type*) [Fintype V] [DecidableEq V]
    (G : SimpleGraph V) [DecidableRel G.Adj]
    (h2ec : ∀ v : V, 2 ≤ G.degree v) :
    ∃ (cycles : Multiset (Finset (Sym2 V))),
      (∀ C ∈ cycles, C ⊆ G.edgeFinset) ∧
      ∀ e ∈ G.edgeFinset,
        Multiset.countP (fun C => e ∈ C) cycles = 2 := by
  sorry

The multiset members are arbitrary edge subsets, with no cycle condition; degree≥2 is also not 2-edge-connectedness.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Assume the intended bridgeless/2-edge-connected graph condition and require every multiset member to be the edge set of a genuine cycle, with each edge counted twice.

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.