In
graph theory, a
factor of a graph
G is a
spanning subgraph, i.e., a subgraph that has the same vertex set as
G. A
k-factor of a graph is a spanning
k-
regular subgraph, and a
k-factorization partitions the edges of the graph into disjoint
k-factors. A graph
G is said to be
k-factorable if it admits a
k-factorization. In particular, a
1-factor is a
perfect matching, and a 1-factorization of a
k-
regular graph is an
edge coloring with
k colors. A
2-factor is a collection of
cycles that spans all vertices of the graph.