OpenAI reports a proof of Barnette’s conjecture
- Mathematics
- Theoretical Computer Science
OpenAI reports that every finite simple cubic bipartite planar graph that is 3-vertex-connected has a Hamiltonian cycle.
Barnette’s Hamiltonian-cycle conjecture
- Mathematics
Does every 3-vertex-connected cubic bipartite planar graph contain a cycle through every vertex?
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Understand the problem ↓Understanding the problem
Read the background
Does every 3-vertex-connected cubic bipartite planar graph contain a cycle through every vertex? OpenAI reports a proof of this 1969 conjecture.
Why it matters
If correct, resolves Barnette’s longstanding Hamiltonian-cycle conjecture for the full stated graph class.
What counts as progress
A proof for every finite simple cubic bipartite planar 3-vertex-connected graph, with the AI origin and exact checking scope documented.
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