{"paper":{"title":"The maximum number of perfect matchings of semi-regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G.L. Wang, Hongliang Lu","submitted_at":"2015-09-02T06:29:33Z","abstract_excerpt":"Let $n\\ge 34$ be an even integer, and $D_n=2\\lceil n/4 \\rceil-1$. In this paper, we prove that every $\\{D_n,\\,D_n+1\\}$-graph of order $n$ contains $\\lceil n/4 \\rceil$ disjoint perfect matchings. This result is sharp in the sense that (i) there exists a $\\{D_n,\\,D_n+1\\}$-graph containing exactly $\\lceil n/4 \\rceil$ disjoint perfect matchings, and that (ii) there exists a $\\{D_n-1,\\,D_n\\}$-graph without perfect matchings for each $n$. As a consequence, for any integer $D\\ge D_n$, every $\\{D,\\,D+1\\}$-graph of order $n$ contains $\\lceil (D+1)/2 \\rceil$ disjoint perfect matchings. This extends Csab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00569","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"}