An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings - Godsil, Christopher David (Ars mathematica contemporanea, 2017)
We give a proof that the largest set of perfect matchings, in which any two contain a common edge, is the set of all perfect matchings that contain a fixed edge. This is a version of the famous Erdős-Ko-Rado theorem for perfect matchings. The proof given in this paper is algebraic, we first determine the least eigenvalue of the perfect matching derangement graph and then use properties of the perfect matching polytope to prove the result.
Keywords: Erdős-Ko-Radov izrek; grafi; neodvisne množice; popolno prirejanje