Tait's conjecture
Tait'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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