{"paper":{"title":"On degree bounds of $k$-uniform hypergraphs with bounded matching number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Haixiang Zhang, Mei Lu, Mengyu Cao","submitted_at":"2026-05-20T14:04:54Z","abstract_excerpt":"We study the connection between the degree sequence of a $k$-uniform hypergraph and the size of its largest matching. Let $\\mathcal{F}$ be a $k$-uniform hypergraph on $n$ vertices and let $d_1 \\ge d_2 \\ge \\dots \\ge d_n$ be the vertex degrees arranged in non-increasing order. For integers $k\\ge 2$, $s\\ge 2$ and $n > 2sk$, we prove that if the $(2sk+1)$-th largest degree satisfies $d_{2sk+1} > \\binom{n-1}{k-1} - \\binom{n-s}{k-1},$ then $\\mathcal{F}$ contains a matching of size at least $s$. This can be viewed as a generalization of theorems by Lu, Guo, and Jiang (2023) and Huang and Rao (2026). "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21208","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/2605.21208/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"}