{"paper":{"title":"Point Set Embeddability with List Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.CG","authors_text":"Boris Klemz, Joseph Dorfer, Lena Schlipf, Matthias Pfretzschner, Thomas Depian","submitted_at":"2026-07-27T09:04:34Z","abstract_excerpt":"Deciding whether a given graph admits a planar straight-line drawing where each vertex is placed on some point from a given finite point set is known as Point Set Embeddability and is a classical problem in graph drawing. In this paper, we study the more general embeddability question where the placement of each vertex $v$ is restricted to a list $L(v)$ of admissible points. We first study the case where the given point set is in convex position. We show that this case is NP-hard even if the given graph is a matching and bi-labeled, i.e., each vertex has at most 2 admissible points. On the pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24182","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24182/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}