Every cubic 3-connected planar bipartite graph is Hamiltonian.
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Statement
Every 3-connected cubic planar bipartite graph has a Hamiltonian cycle (Barnette).
Assessment
Renown 3/5
The surviving refinement after Tutte's related conjecture fell to counterexample in 1946 and Tait's to Tutte himself.
Attackability 2/5
Finite witness with a Hamiltonicity oracle (exponential but feasible to ~90 vertices); exhaustively verified through 90 vertices, which is exactly why the open region is expensive.
- finite witness
- 5/5
- oracle cost
- 2/5
- freshness
- 1/5
- seedability
- 2/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.