{"paper":{"title":"Packing Plane Spanning Trees into a Point Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Ahmad Biniaz, Alfredo Garc\\'ia","submitted_at":"2018-03-06T19:11:36Z","abstract_excerpt":"Let $P$ be a set of $n$ points in the plane in general position. We show that at least $\\lfloor n/3\\rfloor$ plane spanning trees can be packed into the complete geometric graph on $P$. This improves the previous best known lower bound $\\Omega\\left(\\sqrt{n}\\right)$. Towards our proof of this lower bound we show that the center of a set of points, in the $d$-dimensional space in general position, is of dimension either $0$ or $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02385","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"}