{"paper":{"title":"Uniqueness of the extreme cases in theorems of Drisko and Erd\\H{o}s-Ginzburg-Ziv","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dani Kotlar, Ran Ziv, Ron Aharoni","submitted_at":"2015-11-18T13:46:44Z","abstract_excerpt":"Drisko \\cite{drisko} proved (essentially) that every family of $2n-1$ matchings of size $n$ in a bipartite graph possesses a partial rainbow matching of size $n$. In \\cite{bgs} this was generalized as follows: Any $\\lfloor \\frac{k+2}{k+1} n \\rfloor -(k+1)$ matchings of size $n$ in a bipartite graph have a rainbow matching of size $n-k$. We extend this latter result to matchings of not necessarily equal cardinalities.\n  Settling a conjecture of Drisko, we characterize those families of $2n-2$ matchings of size $n$ in a bipartite graph that do not possess a rainbow matching of size $n$. Combinin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05775","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"}