{"paper":{"title":"On Ryser's Conjecture for Linear Intersecting Multipartite Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan D. McKay, Ian M. Wanless, Nevena Franceti\\'c, Sarada Herke","submitted_at":"2015-08-05T01:42:45Z","abstract_excerpt":"Ryser conjectured that $\\tau\\le(r-1)\\nu$ for $r$-partite hypergraphs, where $\\tau$ is the covering number and $\\nu$ is the matching number. We prove this conjecture for $r\\le9$ in the special case of linear intersecting hypergraphs, in other words where every pair of lines meets in exactly one vertex. Aharoni formulated a stronger version of Ryser's conjecture which specified that each $r$-partite hypergraph should have a cover of size $(r-1)\\nu$ of a particular form. We provide a counterexample to Aharoni's conjecture with $r=13$ and $\\nu=1$. We also report a number of computational results. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00951","kind":"arxiv","version":3},"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"}