{"paper":{"title":"Multilevel Planarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Guido Br\\\"uckner, Lukas Barth, Marcel Radermacher, Paul Jungeblut","submitted_at":"2018-10-31T14:18:11Z","abstract_excerpt":"In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\\ell: V \\to \\mathcal P(\\mathbb Z)$ be a function that assigns a finite set of integers to each vertex. A multilevel-planar drawing of $G$ is a planar drawing of $G$ such that the $y$-coordinate of each vertex $v \\in V$ is $y(v) \\in \\ell(v)$, and each edge is drawn as a strictly $y$-monotone curve. We present linear-time algorithms for testing multilevel planarity of embedded graphs with a single source a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13297","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"}