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An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings. (English) Zbl 1370.05102
Summary: In this paper 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.

MSC:
05C35 Extremal problems in graph theory
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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