Combinatorics · Oct 6, 2026
Barnette Hamiltonicity 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.
Scope and what remains
Not the Caccetta–Häggkvist directed cycle-length conjecture.
Contributors
OpenAI source publisher and an unnamed unreleased internal model. Exact paper-level human roles are not disclosed by the family summary.
AI systems: Unreleased OpenAI model