{"paper":{"title":"A generalization 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":"Christos Pelekis, Israel Rocha","submitted_at":"2017-10-12T17:36:47Z","abstract_excerpt":"Let $\\mathcal{H}=(V,\\mathcal{E})$ be an $r$-uniform hypergraph on $n$ vertices and fix a positive integer $k$ such that $1\\le k\\le r$. A $k$-\\emph{matching} of $\\mathcal{H}$ is a collection of edges $\\mathcal{M}\\subset \\mathcal{E}$ such that every subset of $V$ whose cardinality equals $k$ is contained in at most one element of $\\mathcal{M}$. The $k$-matching number of $\\mathcal{H}$ is the maximum cardinality of a $k$-matching. A well-known problem, posed by Erd\\H{o}s, asks for the maximum number of edges in an $r$-uniform hypergraph under constraints on its $1$-matching number. In this articl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04633","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"}