{"paper":{"title":"Covers in Partitioned Intersecting Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C.J. Argue, Ron Aharoni","submitted_at":"2014-12-09T19:38:12Z","abstract_excerpt":"Given an integer $r$ and a vector $\\vec{a}=(a_1, \\ldots ,a_p)$ of positive numbers with $\\sum_{i \\le p} a_i=r$, an $r$-uniform hypergraph $H$ is said to be $\\vec{a}$-partitioned if $V(H)=\\bigcup_{i \\le p}V_i$, where the sets $V_i$ are disjoint, and $|e \\cap V_i|=a_i$ for all $e \\in H,~~i \\le p$. A $\\vec{1}$-partitioned hypergraph is said to be $r$-partite. Let $t(\\vec{a})$ be the maximum, over all intersecting $\\vec{a}$-partitioned hypergraphs $H$, of the minimal size of a cover of $H$. A famous conjecture of Ryser is that $t(\\vec{1})\\le r-1$. Tuza conjectured that if $r>2$ then $t(\\vec{a})=r$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3067","kind":"arxiv","version":2},"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"}