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Tait's conjecture
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.
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• MATHEMATICS
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