On intersecting families of subgraphs of perfect matchings

The seminal Erdos-Ko-Rado (EKR) theorem states that if F is a family of k-subsets of an nelement set X for k <= n/2 such that every pair of subsets in F has a nonempty intersection, then F can be no bigger than the trivially intersecting family obtained by including all ksubsets of X that contain a fixed element x is an element of X. This family is called the star centered at x. In this paper, we formulate and prove an EKR theorem for intersecting families of subgraphs of the perfect matching graph. This can be considered a generalization not only of the aforementioned EKR theorem but also of a signed variant of it, first stated by Meyer [9], and proved separately by Deza-Frankl [3] and Bollob & aacute;s-Leader [1]. The proof of our main theorem relies on a novel extension of Katona's beautiful cycle method. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.