{"paper":{"title":"Compatible Connectivity-Augmentation of Planar Disconnected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Fabrizio Frati, Greg Aloupis, Luis Barba, Pat Morin, Paz Carmi, Vida Dujmovi\\'c","submitted_at":"2014-08-11T15:24:32Z","abstract_excerpt":"Motivated by applications to graph morphing, we consider the following \\emph{compatible connectivity-augmentation problem}: We are given a labelled $n$-vertex planar graph, $\\mathcal{G}$, that has $r\\ge 2$ connected components, and $k\\ge 2$ isomorphic planar straight-line drawings, $G_1,\\ldots,G_k$, of $\\mathcal{G}$. We wish to augment $\\mathcal G$ by adding vertices and edges to make it connected in such a way that these vertices and edges can be added to $G_1,\\ldots,G_k$ as points and straight-line segments, respectively, to obtain $k$ planar straight-line drawings isomorphic to the augmenta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2436","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"}