{"paper":{"title":"Recognizing IC-Planar and NIC-Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Franz J. Brandenburg","submitted_at":"2016-10-27T17:01:18Z","abstract_excerpt":"We prove that triangulated IC-planar and NIC-planar graphs can be recognized in cubic time.\n  A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge. A drawing is IC-planar if, in addition, each vertex is incident to at most one crossing edge and NIC-planar if two pairs of crossing edges share at most one vertex. In a triangulated drawing each face is a triangle. In consequence, planar-maximal and maximal IC-planar and NIC-planar graphs can be recognized in O(n^5) time and maximum and optimal ones in O(n^3) time. In contrast, recognizing 3-connected IC-planar an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08884","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"}