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.

External Links

• sci.math posting by Bill Taylor on Tutte's fragment (http://www.math.niu.edu/%7Erusin/known-math/97/tutte)
• Peter Guthrie Tait (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Tait)