High Quality Content by WIKIPEDIA articles! In mathematics, Tait's
conjecture states that "Every 3-connected planar cubic graph has a
Hamiltonian cycle (along the edges) through all its vertices." It
was proposed by P. G. Tait (1884) and disproved by W. T. Tutte
(1946), who constructed a counterexample with 25 faces, 69 edges
and 46 vertices. Several smaller counterexamples, with 21 faces, 57
edges and 38 vertices, were later proved minimal by Holton &
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