Tait's conjecture

Tait's conjecture is a hypothesis put forward Peter Tait in 1884, which says that every polyhedron has a Hamiltonian cycle through its vertices. In other words, it is possible to travel around all the edges of a polyhedron, passing through each vertex (corner) exactly once and arriving back at the starting point. If true, Tait's Conjecture would have provided an immediate proof of the four-color theorem. However, in 1946, the British mathematician William Tutte (1917–2002), whose work at Bletchley Park on cracking the German FISH cipher played an important role in World War II, found a counterexample to the conjecture in the form of a polygon with 25 faces, 69 edges, and 46 vertices.