{"paper":{"title":"Every Large Point Set contains Many Collinear Points or an Empty Pentagon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Attila P\\'or, Brad Ballinger, David R. Wood, Ferran Hurtado, Prosenjit Bose, Scott D. Kominers, S\\'ebastien Collette, Stefan Langerman, Vida Dujmovi\\'c, Zachary Abel","submitted_at":"2009-04-01T22:49:26Z","abstract_excerpt":"We prove the following generalised empty pentagon theorem: for every integer $\\ell \\geq 2$, every sufficiently large set of points in the plane contains $\\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the \"big line or big clique\" conjecture of K\\'ara, P\\'or, and Wood [\\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0262","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"}