# 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.