{"paper":{"title":"Beyond Outerplanarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Alexander Wolff, Andre L\\\"offler, Giuseppe Liotta, Myroslav Kryven, Steven Chaplick","submitted_at":"2017-08-29T12:26:43Z","abstract_excerpt":"We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., \\emph{convex drawings}. We consider two families of graph classes with convex drawings: \\emph{outer $k$-planar} graphs, where each edge is crossed by at most $k$ other edges; and \\emph{outer $k$-quasi-planar} graphs, where no $k$ edges can mutually cross.\n  We show that the outer $k$-planar graphs are $\\lfloor3.5\\sqrt{k}\\rfloor$-degenerate, and consequently that every outer $k$-planar graph can be colored with $\\lfloor3.5\\sqrt{k}\\rfloor + 1$ colors. We further show that every outer $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08723","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/1708.08723/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"}