Let be a Graph and a Subgraph of . Let the number of Odd components in be denoted , and the number of Vertices of . The condition for every Subset of Vertices is Necessary and Sufficient for to have a 1-Factor.
See also Factor (Graph)
References
Honsberger, R. ``Lovász' Proof of a Theorem of Tutte.'' Ch. 14 in Mathematical Gems II.
Washington, DC: Math. Assoc. Amer., pp. 147-157, 1976.
Tutte, W. T. ``The Factorization of Linear Graphs.'' J. London Math. Soc. 22, 107-111, 1947.