{"paper":{"title":"Semi-perfect 1-Factorizations of the Hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Natalie C. Behague","submitted_at":"2018-11-15T14:29:34Z","abstract_excerpt":"A 1-factorization $\\mathcal{M} = \\{M_1,M_2,\\ldots,M_n\\}$ of a graph $G$ is called perfect if the union of any pair of 1-factors $M_i, M_j$ with $i \\ne j$ is a Hamilton cycle. It is called $k$-semi-perfect if the union of any pair of 1-factors $M_i, M_j$ with $1 \\le i \\le k$ and $k+1 \\le j \\le n$ is a Hamilton cycle.\n  We consider 1-factorizations of the discrete cube $Q_d$. There is no perfect 1-factorization of $Q_d$, but it was previously shown that there is a 1-semi-perfect 1-factorization of $Q_d$ for all $d$. Our main result is to prove that there is a $k$-semi-perfect 1-factorization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06389","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.06389/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}