{"paper":{"title":"New results on the coarseness of bicolored point sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.MG"],"primary_cat":"math.CO","authors_text":"I. Ventura, J. M. D\\'iaz-B\\'a\\~nez, P. P\\'erez-Lantero, R. Fabila-Monroy","submitted_at":"2012-11-09T00:54:29Z","abstract_excerpt":"Let $S$ be a 2-colored (red and blue) set of $n$ points in the plane. A subset $I$ of $S$ is an island if there exits a convex set $C$ such that $I=C\\cap S$. The discrepancy of an island is the absolute value of the number of red minus the number of blue points it contains. A convex partition of $S$ is a partition of $S$ into islands with pairwise disjoint convex hulls. The discrepancy of a convex partition is the discrepancy of its island of minimum discrepancy. The coarseness of $S$ is the discrepancy of the convex partition of $S$ with maximum discrepancy. This concept was recently defined "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2020","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"}