{"paper":{"title":"Rainbow matchings and partial transversals of Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andras Gyarfas, Gabor N. Sarkozy","submitted_at":"2012-08-28T14:05:43Z","abstract_excerpt":"In this paper we consider properly edge-colored graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A matching is called \\it rainbow \\rm if its edges have different colors. The minimum degree of a graph is denoted by $\\delta(G)$. We show that properly edge colored graphs $G$ with $|V(G)|\\ge 4\\delta(G)-3$ have rainbow matchings of size $\\delta(G)$, this gives the best known estimate to a recent question of Wang. Since one obviously needs at least $2\\delta(G)$ vertices to guarantee a rainbow matching of size $\\delta(G)$, we investigate what hap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5670","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"}