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.