{"paper":{"title":"Further Consequences of the Colorful Helly Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Edgardo Rold\\'an-Pensado, Leonardo Mart\\'inez-Sandoval, Natan Rubin","submitted_at":"2018-03-16T13:47:05Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of convex sets in ${\\mathbb R}^d$, which are colored with $d+1$ colors. We say that $\\mathcal{F}$ satisfies the Colorful Helly Property if every rainbow selection of $d+1$ sets, one set from each color class, has a non-empty common intersection. The Colorful Helly Theorem of Lov\\'asz states that for any such colorful family $\\mathcal{F}$ there is a color class $\\mathcal{F}_i\\subset \\mathcal{F}$, for $1\\leq i\\leq d+1$, whose sets have a non-empty intersection.\n  We establish further consequences of the Colorful Helly hypothesis. In particular, we show that for each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06229","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"}