Hamiltonian decomposable graph

Hamiltonian decomposable graph --- гамильтоново разложимый граф.

A graph [math]\displaystyle{ G }[/math] is Hamiltonian decomposable if either the degree of [math]\displaystyle{ G }[/math] is [math]\displaystyle{ 2k }[/math] and the edges of [math]\displaystyle{ G }[/math] can be partitioned into [math]\displaystyle{ k }[/math] hamiltonian cycles, or the degree of [math]\displaystyle{ G }[/math] is [math]\displaystyle{ 2k+1 }[/math] and the edges of [math]\displaystyle{ G }[/math] can be partitioned into [math]\displaystyle{ k }[/math] hamiltonian cycles and a 1-factor. If [math]\displaystyle{ G }[/math] is a Hamiltonian decomposable graph, then [math]\displaystyle{ G }[/math] is loopless, connected, and regular. For a graph [math]\displaystyle{ G }[/math] to have a hamiltonian decomposition that the graph [math]\displaystyle{ G }[/math], it should have a hamiltonian cycle.