{"paper":{"title":"Erd\\H{o}s-Ko-Rado for Perfect Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Lindzey","submitted_at":"2014-09-06T20:54:21Z","abstract_excerpt":"A perfect matching of a complete graph $K_{2n}$ is a 1-regular subgraph that contains all the vertices. Two perfect matchings intersect if they share an edge. It is known that if $\\mathcal{F}$ is family of intersecting perfect matchings of $K_{2n}$, then $|\\mathcal{F}| \\leq (2(n-1) - 1)!!$ and if equality holds, then $\\mathcal{F} = \\mathcal{F}_{ij}$ where $ \\mathcal{F}_{ij}$ is the family of all perfect matchings of $K_{2n}$ that contain some fixed edge $ij$. We give a short algebraic proof of this result, resolving a question of Godsil and Meagher. Along the way, we show that if a family $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2057","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}