Petersen coloring conjecture

3 selected milestones · Source coverage checked 2026-10-14 · Historical annotation and mathematical review remain separate.

1. 1985 publication

   Foundation

   The normal-five formulation

   Jaeger’s earlier work establishes the coloring equivalence recalled in Proposition 2.1.

   Statements & sources

   • Petersen and normal-five colorings are equivalent →

   • A 112-Vertex Counterexample to the Petersen Coloring Conjecture ↗Introduction; Proposition 2.1; references to Jaeger (1985, 1988)

   Historical annotation review: pending. The date refers to the publication, with the precision supported by the source.

2. 1988 publication

   Foundation

   Jaeger’s coloring question

   The selected paper attributes the bridgeless cubic question to Jaeger’s 1988 chapter.

   Statements & sources

   • Every bridgeless cubic graph admits a Petersen coloring →

   • A 112-Vertex Counterexample to the Petersen Coloring Conjecture ↗Introduction; Proposition 2.1; references to Jaeger (1985, 1988)

   Historical annotation review: pending. The date refers to the publication, with the precision supported by the source.

3. Aug 8, 2026 preprint

   Related result

   Two explicit counterexamples and certificates

   Putman publishes the graph constructions, encodings and external checks; the frozen release is version 1.1.0.

   Statements & sources

   • The main 112-vertex counterexample →
   • A distinct symmetric 112-vertex counterexample →

   • A 112-Vertex Counterexample to the Petersen Coloring Conjecture ↗Theorem 1.1; Section 3; Appendix A
   • A 112-Vertex Counterexample to the Petersen Coloring Conjecture ↗Theorem 6.1; Section 6
   • Petersen counterexample: frozen construction and certificates ↗03_CERTIFICATION, 04_OPTIONAL_D3 and 05_DOCUMENTATION

   Historical annotation review: pending. The date refers to the preprint, with the precision supported by the source.

Scope & review: This is a selected source-supported milestone, not an exhaustive history.