{"paper":{"title":"On balanced 4-holes in bichromatic point sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"A. Ram\\'irez-Vigueras, I. Ventura, J. M. D\\'iaz-B\\'a\\~nez, J. Urrutia, P. P\\'erez-Lantero, R. Fabila-Monroy, S. Bereg, T. Sakai","submitted_at":"2017-08-03T22:12:15Z","abstract_excerpt":"Let $S=R\\cup B$ be a point set in the plane in general position such that each of its elements is colored either red or blue, where $R$ and $B$ denote the points colored red and the points colored blue, respectively. A quadrilateral with vertices in $S$ is called a $4$-hole if its interior is empty of elements of $S$. We say that a $4$-hole of $S$ is balanced if it has $2$ red and $2$ blue points of $S$ as vertices. In this paper, we prove that if $R$ and $B$ contain $n$ points each then $S$ has at least $\\frac{n^2-4n}{12}$ balanced $4$-holes, and this bound is tight up to a constant factor. S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01321","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"}