{"paper":{"title":"An Asymptotic Version of the Multigraph 1-Factorization Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. R. Vaughan","submitted_at":"2010-10-25T17:11:41Z","abstract_excerpt":"We give a self-contained proof that for all positive integers $r$ and all $\\epsilon > 0$, there is an integer $N = N(r, \\epsilon)$ such that for all $n \\ge N$ any regular multigraph of order $2n$ with multiplicity at most $r$ and degree at least $(1+\\epsilon)rn$ is 1-factorizable. This generalizes results of Perkovi{\\'c} and Reed, and Plantholt and Tipnis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5192","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"}