Proved
Infinite family consequence reported ↗
Uses the separate Ma–Mattiolo–Steffen–Wolf theorem.
Source dated Aug 8, 2026 · Observed Oct 14, 2026
Theorem · version 1
Infinitely many Petersen-coloring counterexamples
Statement
Infinitely many connected simple bridgeless cubic graphs admit no Petersen coloring.
Assumptions
- Corollary 5.1 combines the finite counterexample with the universal-target theorem of Ma, Mattiolo, Steffen and Wolf.
Evidence
Source reports
Connections
In this problem · publication v3 · Selected context
Petersen coloring conjecture →
Related result · Proved
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v7
Petersen coloring conjecture →
Related result · Proved
Relationship not independently reviewed. This concerns its use in this problem.
Sources
A 112-Vertex Counterexample to the Petersen Coloring Conjecture →
- Corollary 5.1; Ma–Mattiolo–Steffen–Wolf (2025) → · Original passage ↗
Recorded wording
The finite counterexample together with the cited universal-target theorem implies infinitely many connected simple bridgeless cubic counterexamples.
paraphrase · Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.
Bryce Putman · Preprint · Publication date Aug 8, 2026
Source-reported results and external checks are separate from independent OpenMath assessment.
Revision & attribution
Source revision: v1. Observed Oct 14, 2026.
Putman reports extensive OpenAI-model assistance in discovery, search, verification and preparation; he reviewed the final claims and artifacts and accepts responsibility.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Infinite family consequence reported ↗
Uses the separate Ma–Mattiolo–Steffen–Wolf theorem.
Source dated Aug 8, 2026 · Observed Oct 14, 2026 · Source passage →
Record details
- Claim ID
- claim-petersen-infinitely-many-counterexamples
- Statement version
- 1
- SHA-256
- 87a5dfde00a4ec4a59ef94dcb7a47ceb2a4ff33114ef5b880031c15d2547c3f7