{"paper":{"title":"On the Parameterized Complexity of Bounded-Density Vertex Deletion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andr\\'e Nichterlein, Anton Herrmann, Jakob Raupach, Tom-Lukas Breitkopf","submitted_at":"2026-06-24T16:31:03Z","abstract_excerpt":"We explore the parameterized complexity of Bounded Density Vertex Deletion (BDVD): given a graph $G$, an integer budget $k$, and a target density $\\tau_\\rho$, the task is to determine whether the density (i.e. number of edges divided by number of vertices) of the densest subgraph of $G$ can be reduced to at most $\\tau_\\rho$ by deleting at most $k$ vertices. Our primary focus is on structural graph parameters related to treewidth, as the parameterized complexity of BDVD with respect to treewidth was left as open question by Bazgan et al. [JCSS, 2025]. We resolve this question by showing W[1]-ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26012","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/2606.26012/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"}