{"paper":{"title":"Coloring Planar Homothets and Three-Dimensional Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jean Cardinal, Matias Korman","submitted_at":"2011-01-03T17:06:52Z","abstract_excerpt":"The inclusion relation between simple objects in the plane may be used to define geometric set systems, or hypergraphs. Properties of various types of colorings of these hypergraphs have been the subject of recent investigations, with applications to wireless networking.\n  We first prove that every set of homothetic copies of a given convex body in the plane can be colored with four colors so that any point covered by at least two copies is covered by two copies with distinct colors. This generalizes a previous result from Smorodinsky [18]. As a corollary, we find improvements to well studied "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0565","kind":"arxiv","version":8},"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"}