{"paper":{"title":"Rainbow sets in the intersection of two matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Kotlar, Ran Ziv, Ron Aharoni","submitted_at":"2014-05-13T12:07:25Z","abstract_excerpt":"Given sets $F_1, \\ldots ,F_n$, a {\\em partial rainbow function} is a partial choice function of the sets $F_i$. A {\\em partial rainbow set} is the range of a partial rainbow function. Aharoni and Berger \\cite{AhBer} conjectured that if $M$ and $N$ are matroids on the same ground set, and $F_1, \\ldots ,F_n$ are pairwise disjoint sets of size $n$ belonging to $M \\cap N$, then there exists a rainbow set of size $n-1$ belonging to $M \\cap N$. Following an idea of Woolbright and Brower-de Vries-Wieringa, we prove that there exists such a rainbow set of size at least $n-\\sqrt{n}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3119","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"}