{"paper":{"title":"The Complexity of Drawing Graphs on Few Lines and Few Planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.CC","authors_text":"Alexander Ravsky, Alexander Wolff, Fabian Lipp, Krzysztof Fleszar, Oleg Verbitsky, Steven Chaplick","submitted_at":"2016-07-21T19:50:36Z","abstract_excerpt":"It is well known that any graph admits a crossing-free straight-line drawing in $\\mathbb{R}^3$ and that any planar graph admits the same even in $\\mathbb{R}^2$. For a graph $G$ and $d \\in \\{2,3\\}$, let $\\rho^1_d(G)$ denote the smallest number of lines in $\\mathbb{R}^d$ whose union contains a crossing-free straight-line drawing of $G$. For $d=2$, $G$ must be planar. Similarly, let $\\rho^2_3(G)$ denote the smallest number of planes in $\\mathbb{R}^3$ whose union contains a crossing-free straight-line drawing of $G$.\n  We investigate the complexity of computing these three parameters and obtain th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06444","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1607.06444/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}