{"paper":{"title":"On the stab number of rectangle intersection graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Dibyayan Chakraborty, Mathew C. Francis","submitted_at":"2018-04-18T06:50:27Z","abstract_excerpt":"We introduce the notion of \\emph{stab number} and \\emph{exact stab number} of rectangle intersection graphs, otherwise known as graphs of boxicity at most 2. A graph $G$ is said to be a \\emph{$k$-stabbable rectangle intersection graph}, or \\emph{$k$-SRIG} for short, if it has a rectangle intersection representation in which $k$ horizontal lines can be chosen such that each rectangle is intersected by at least one of them. If there exists such a representation with the additional property that each rectangle intersects exactly one of the $k$ horizontal lines, then the graph $G$ is said to be a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06571","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"}