{"paper":{"title":"Order-preserving 1-string representations of planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Martin Derka, Therese Biedl","submitted_at":"2016-09-26T19:30:37Z","abstract_excerpt":"This paper considers 1-string representations of planar graphs that are order-preserving in the sense that the order of crossings along the curve representing vertex $v$ is the same as the order of edges in the clockwise order around $v$ in the planar embedding. We show that this does not exist for all planar graphs (not even for all planar 3-trees), but show existence for some subclasses of planar partial 3-trees. In particular, for outer-planar graphs it can be order-preserving and outer-string in the sense that all ends of strings are on the outside of the representation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08132","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"}