Definitions for "1-factorable"
In graph theory, a 1-factor of a graph is a collection of disjoint edges (a matching). A 1-factorization of a graph G is a collection of 1-factors such that every edge of G is in exactly one of these 1-factors. The graph is thus "factored" into edge-disjoint subgraphs; in each subgraph, each vertex is the endpoint of exactly one edge.