{"paper":{"title":"Drawing Reeb Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Brittany Terese Fasy, Erfan Hosseini Sereshgi, Erin Chambers, Maarten L\\\"offler","submitted_at":"2025-04-30T05:35:04Z","abstract_excerpt":"Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we bridge an essential gap in the literature by exploring the complexity of drawing Reeb graphs. Specifically, we demonstrate that Reeb graph crossing number minimization is NP-hard, both for straight-lined and curved edges. On the other hand, we identify specific classes of Reeb graphs, namely paths and caterpillars, for which crossing-free drawings exist. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.21329","kind":"arxiv","version":2},"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/2504.21329/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"}