Barnette’s Hamiltonian-cycle conjecture

Proves that every finite simple cubic bipartite planar 3-vertex-connected graph has a Hamiltonian cycle, resolving Barnette's conjecture. Equivalently, every three-edge path in a finite simple cubic 3-vertex-connected bipartite Pfaffian graph lies in a Hamiltonian cycle. (Lean)

Manuscript

Paired states and Hamiltonian cycles in cubic bipartite planar graphs

September 24, 2026 · source · cite as \cite{OAI:Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026}

We prove Barnette's conjecture: every finite simple cubic bipartite planar 3-vertex-connected graph has a Hamiltonian cycle.

Result 180 · Combinatorics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.