{"paper":{"title":"Where Treewidth and Pathwidth Diverge: Towards a Uniform Kernel for Pathwidth-$\\eta$ Deletion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Ahmed Ghazy, Jakob Greilhuber, Roohani Sharma, Tim A. Hartmann","submitted_at":"2026-08-10T16:19:40Z","abstract_excerpt":"For a constant $\\eta \\geq 0$, Pathwidth-$\\eta$ Deletion is the problem of deciding whether, for a given graph $G$ and integer $k$, there is a set $S \\subseteq V(G)$ of size at most $k$ such that the pathwidth of $G - S$ is at most $\\eta$. The problems Treewidth-$\\eta$ Deletion and Treedepth-$\\eta$ Deletion are defined similarly for the parameters treewidth and treedepth, respectively. A landmark result of Fomin et al. [FOCS, 2012] shows that, for any constant $\\eta$, all three problems admit a kernel on $O(k^{c(\\eta)})$ vertices, where $c(\\eta)$ is a constant depending on $\\eta$.\n  Giannopoulo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09800","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/2608.09800/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"}