14 / Mathematics Open investigation
Can every vertex share one journey?
Hamiltonian cycles, graph transformations and Barnette’s conjecture.
This programme explores Hamiltonian cycles in cubic, bipartite, 3-connected planar graphs, using the Barnette problem as a second testbed for research lenses.
The working material includes graph generation, structural checks, proposed strengthenings and adversarial review. Failed reduction ideas remain part of the record.
Where the claim stops.
This is an investigation of the conjecture, not a claimed proof. Literature identifications in working notes must not be promoted to established results.
Source: barnette / README.md. Summary prepared from the local research record, 11 September 2026.
Research led by Aleksei Kudriashov (Alex Komang). Mathematical paper and witness text/data: CC BY 4.0 where stated in the source repository.