# Hamiltonian Path **A [[path]] that visits every vertex exactly once.** ![[HamiltonianPath.svg|367]] *A Hamiltonian path* A [[graph]] with a Hamiltonian path is known as a *traceable* graph. ## Hamiltonian cycle > [!Hamiltonian cycle] > A *Hamiltonian cycle*, or a *Hamiltonian circuit*, is a [[cycle]] in which every vertex is visited exactly once, with the exception of the start and end vertex. A graph containing a Hamiltonian cycle is known as a *Hamiltonian* graph. A [[complete graph]] with more than two vertices is Hamiltonian, as well as every platonic solid when projected as a [[planar graph]]. ![[HamiltonianCycleSchlegelDiagramCube.svg|300]] *The [[Schlegel diagram]] of a cube, which has a Hamiltonian cycle*