A quasi-Hamilton decomposition of a regular graph of odd degree greater than 1 is a partition of its edge set into Hamiltonian cycles and a single perfect matching (Bosák 1990, p. 123). Under the extended convention of Alspach (2010), a graph admitting such a partition is considered Hamilton decomposable. This differs from a Hamilton decomposition, which consists entirely of Hamiltonian cycles.
Quasi-Hamilton Decomposition
See also
Hamilton Decomposable Graph, Hamilton Decomposition, Hamiltonian Cycle, Perfect Matching, Regular GraphExplore with Wolfram|Alpha
References
Alspach, B. "Three Hamilton Decomposition Problems." University of Western Australia. May 11, 2010. https://symomega.wordpress.com/wp-content/uploads/2010/05/talk8.pdf.Bosák, J. Decompositions of Graphs. New York: Springer, 1990.Referenced on Wolfram|Alpha
Quasi-Hamilton DecompositionCite this as:
Weisstein, Eric W. "Quasi-Hamilton Decomposition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Quasi-HamiltonDecomposition.html