Hamilton circuit | Hamilton cycle | Hamiltonian circuit | traveler's problem

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node exactly once. A graph possessing a Hamiltonian cycle is said to be a Hamiltonian graph. By convention, the singleton graph K_1 is considered to be Hamiltonian even though it does not posses a Hamiltonian cycle, while the connected graph on two nodes K_2 is not. The Hamiltonian cycle is named after Sir William Rowan Hamilton, who devised a puzzle in which such a path along the polyhedron edges of an dodecahedron was sought (the Icosian game).

Chvátal's theorem | Dirac's theorem | Euler graph | Eulerian cycle | Grinberg formula | Hamiltonian graph | Hamiltonian path | Hamiltonian walk | Herschel graph | icosian game | Kozyrev-Grinberg theory | longest path | middle levels conjecture | Ore's theorem | Pósa's theorem | Smith's network theorem | tour | traveling salesman problem | unicursal circuit | uniquely Hamiltonian graph