Tutte's theorem may refer to several theorems of W. T. Tutte, including: Tutte's theorem on Hamiltonian cycles, the existence of Hamiltonian cycles in 4-vertex-connected planar graphs Tutte's theorem on perfect matchings, a characterization of the graphs having perfect matchings Tutte's spring theorem, on the planarity and uniqueness of graph drawings obtained from systems of idealized springs Tutte homotopy theorem, on the composition of generalized paths in matroids
See also Hanani–Tutte theorem on the parity of edge crossings in graph drawings