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 possess 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). The problem of enumerating Hamiltonian cycles in specific classes of graphs is one of the most difficult problems in enumerative combinatorics .
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
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