{"paper":{"title":"Polyline Drawings with Topological Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Emilio Di Giacomo, Fabrizio Montecchiani, Giuseppe Liotta, Henk Meijer, Peter Eades","submitted_at":"2018-09-21T13:44:13Z","abstract_excerpt":"Let $G$ be a simple topological graph and let $\\Gamma$ be a polyline drawing of $G$. We say that $\\Gamma$ \\emph{partially preserves the topology} of $G$ if it has the same external boundary, the same rotation system, and the same set of crossings as $G$. Drawing $\\Gamma$ fully preserves the topology of $G$ if the planarization of $G$ and the planarization of $\\Gamma$ have the same planar embedding. We show that if the set of crossing-free edges of $G$ forms a connected spanning subgraph, then $G$ admits a polyline drawing that partially preserves its topology and that has curve complexity at m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08111","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"}