A graph factor is a spanning subgraph. An 
-factor is a regular
graph of vertex degree 
that spans the original graph. In
particular, a 2-factor of a finite
graph that is a simple graph is a disjoint
union of cycle graphs covering all vertices.
A 1-factor of a graph 
with 
graph vertices is a set of
separate graph
edges which collectively contain all 
of the graph vertices of 
among their endpoints. Harary and Palmer
(1973, p. 270) list the enumeration of 1-factors and factorizations as graphical
enumeration problems.
A one-factorization partitions the edge set of a graph into perfect matchings. It is a perfect one-factorization when every two distinct factors together form a Hamiltonian cycle (Gill and Wanless 2020, p. 177).
." Bull. Austral. Math.
Soc. 101, 177-185, 2020.