{"paper":{"title":"On Pseudo-Convex Partitions of a Planar Point Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bhaswar B. Bhattacharya, Sandip Das","submitted_at":"2010-11-08T18:39:40Z","abstract_excerpt":"Aichholzer et al. [{\\it Graphs and Combinatorics}, Vol. 23, 481-507, 2007] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number $\\psi(n)$ satisfies, $\\frac{3}{4}\\lfloor\\frac{n}{4}\\rfloor\\leq \\psi(n)\\leq\\lceil\\frac{n}{4}\\rceil$. In this paper we prove that $\\psi(13)=3$, which immediately improves the upper bound on $\\psi(n)$ to $\\lceil\\frac{3n}{13}\\rceil$, thus answering a question posed by Aichholzer et al. in the same paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1866","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"}