A Hamilton decomposition (also called a Hamiltonian decomposition; Bosák 1990, p. 123) of a Hamiltonian regular graph is a partition of its edge set into Hamiltonian cycles. The figure above illustrates the six distinct Hamilton decompositions of the pentatope graph K_5. The definition is sometimes extended to a decomposition into Hamiltonian cycles for a regular graph of even degree or into Hamiltonian cycles and a single perfect matching for a regular graph of odd degree, with a decomposition of the latter type being known as a quasi-Hamilton decomposition.
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