Hamilton's Revenge: Barnette's Hamiltonian-cycle conjecture

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Hamilton's Revenge

based on Result #180: Barnette's Hamiltonian-cycle conjecture

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	counting, coloring	Levels:	1
Category:	Combinatorics	Lean version:	YES! ✔
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Barnette’s Hamiltonian-cycle 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.

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LEVEL 1 Paired states and Hamiltonian cycles in cubic bipartite planar graphs

released 2026-09-24 | 2 theorems · 6 lemmas · 11 proofs · 5,618 words | PLAY LEVEL 1 » (pdf)

We prove Barnette's conjecture: every finite simple cubic bipartite planar 3-vertex-connected graph has a Hamiltonian cycle.

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