A Hamilton decomposable graph is a regular graph whose edge set has a Hamilton decomposition, i.e., can be partitioned into Hamiltonian cycles. Under the extended convention of Alspach (2010), a regular graph of odd degree greater than 1 is also considered Hamilton decomposable when its edge set can be partitioned into Hamiltonian cycles and one perfect matching. Such a partition is called a quasi-Hamilton decomposition (Bosák 1990, p. 123).
(Quasi-)Hamilton decomposable graphs in the Wolfram Language can be obtained using GraphData["HamiltonDecomposable"].
