{"paper":{"title":"Drawing Clustered Graphs on Disk Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Ignaz Rutter, Marcel Radermacher, Nina Zimbel, Tamara Mchedlidze","submitted_at":"2018-11-02T09:05:43Z","abstract_excerpt":"Let $G=(V, E)$ be a planar graph and let $\\mathcal{C}$ be a partition of $V$. We refer to the graphs induced by the vertex sets in $\\mathcal{C}$ as Clusters. Let $D_{\\mathcal C}$ be an arrangement of disks with a bijection between the disks and the clusters. Akitaya et al. give an algorithm to test whether $(G, \\mathcal{C})$ can be embedded onto $D_{\\mathcal C}$ with the additional constraint that edges are routed through a set of pipes between the disks. Based on such an embedding, we prove that every clustered graph and every disk arrangement without pipe-disk intersections has a planar stra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00785","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"}