Chris Godsil, Karen Meagher
Published 2015-06-29Version 1
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 Erd\H{o}s-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 use properties of the perfect matching polytope. We also prove that the perfect matching derangement graph is not a Cayley graph.
Spectra of Cayley Graphs of Complex Reflection Groups
Expander property of the Cayley Graphs of $\mathbb{Z}_m \ltimes \mathbb{Z}_n$
On the Cayley graph of a commutative ring with respect to its zero-divisors
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