{"paper":{"title":"Improved Bound on Vertex Degree Version of Erd\\H{o}s Matching Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Mingyang Guo, Yaolin Jiang","submitted_at":"2020-01-09T03:09:38Z","abstract_excerpt":"For a $k$-uniform hypergraph $H$, let $\\delta_1(H)$ denote the minimum vertex degree of $H$, and $\\nu(H)$ denote the size of the largest matching in $H$. In this paper, we show that for any $k\\geq 3$ and $\\beta>0$, there exists an integer $n_0(\\beta,k)$ such that for positive integers $n\\geq n_0$ and $m\\leq (\\frac{k}{2(k-1)}-\\beta)\\frac{n}{k}$, if $H$ is an $n$-vertex $k$-graph with $\\delta_1(H)>{{n-1}\\choose {k-1}}-{{n-m}\\choose {k-1}},$ then $\\nu(H)\\geq m$. This improves upon earlier results of Bollob\\'{a}s, Daykin and Erd\\H{o}s (1976) for the range $n> 2k^3(m+1)$ and Huang and Zhao (2017) f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02820","kind":"arxiv","version":4},"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/2001.02820/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"}