Definition:Hamilton Cycle

Definition

A Hamilton cycle in a graph $G$ is a cycle that contains every vertex of $G$ (but not necessarily every edge).

Also known as

The term Hamilton cycle is sometimes seen rendered as hamilton cycle, that is, without a capital H.

The longer form Hamiltonian cycle (or hamiltonian cycle) is also sometimes encountered.

Some sources use the term Hamilton (or Hamiltonian) circuit.

Also see

• Definition:Hamiltonian Path

Source of Name

This entry was named for William Rowan Hamilton.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 3.2$: The Salesman's Problem: An Introduction to Hamiltonian Graphs
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Hamiltonian circuit
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Hamiltonian cycle