# Hamiltonian graph-class feasibility reference

Family 180: Barnette’s Hamiltonian-cycle conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Routing researchers can record cycle existence for the specified cubic bipartite planar 3-vertex-connected graph class.

## Applicability and commercial boundary

Existence is not an efficient cycle finder or a general travelling-salesperson improvement, and operational graphs may fail the structural assumptions.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Inspect constructive algorithm content and class-testing cost.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Paired states and Hamiltonian cycles in cubic bipartite planar graphs](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Paired-states-and-Hamiltonian-cycles-in-cubic-bipartite-planar-graphs-September-24-2026/paper.pdf).