An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings

2015/06/29 by Chris Godsil, Godsil, Chris, Karen Meagher +1 · 3 citations
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1506.08770

Abstract

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 use properties of the perfect matching polytope. We also prove that the perfect matching derangement graph is not a Cayley graph.

Cited by

• Erdős-Ko-Rado theorem and Hilton-Milner type theorem for k-partitions
• Cross-intersection theorems for uniform partitions of finite sets
• A Composition-Based Approach to EKR Problems

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