In this case the set of the cycles constitutes a spanning subgraph of G.

A k-factor is a k-regular spanning subgraph.

A spanning subgraph of a given graph G has the same set of vertices as G itself but, possibly, fewer edges.

The same holds for graphs that have a maximal outerplanar spanning subgraph, as do for instance the wheel graphs.

A spanning subgraph of a given graph G may be defined from any subset S of the edges of G.

A k-spanner is a spanning subgraph, S, in which every two vertices are at most k times as far apart on S than on G.

And because it contains a hypercube as a spanning subgraph, it inherits from the hypercube all monotone graph properties, such as the property of containing a Hamiltonian cycle.