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Tait's conjectureTait's conjecture states that "Every polyhedron has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed in 1886 by P. G. Tait and disproved in 1946, when W. T. Tutte constructed a counterexample with 25 faces, 69 edges and 46 vertices.The conjecture could have been significant, because if true, it would have implied the four color theorem. 
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Tait's conjecture".