{"paper":{"title":"Domination in intersecting hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Liying Kang, Shan Li, Yanxia Dong","submitted_at":"2017-01-06T08:17:35Z","abstract_excerpt":"A matching in a hypergraph $H$ is a set of pairwise disjoint hyperedges. The matching number $\\alpha'(H)$ of $H$ is the size of a maximum matching in $H$. A subset $D$ of vertices of $H$ is a dominating set of $H$ if for every $v\\in V\\setminus D$ there exists $u\\in D$ such that $u$ and $v$ lie in an hyperedge of $H$. The cardinality of a minimum dominating set of $H$ is called the domination number of $H$, denoted by $\\gamma(H)$. It is known that for a intersecting hypergraph $H$ with rank $r$, $\\gamma(H)\\leq r-1$. In this paper we present structural properties on intersecting hypergraphs with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01564","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"}