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We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G = (V, E), k); |V| = n, we can construct, in polynomial time, an instance (G', k') such that (i) (G, k) is a YES instance if and only if (G', k') is a YES instance, (ii)"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.0806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-04T05:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"c3abc47ad0a15451d25874c25c850a1723133fbffbd7251252c43e36666c0948","abstract_canon_sha256":"8e7f2b6cf08eed9725d93054b61cb2564359f536889b0e137ca3f7252d34007c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:24.569989Z","signature_b64":"BkU13KUrJvEutLjBbXgtaKfxKhpD9PJ28dJ+jwHmqx4GKReSzE/VBwEl+U4sv9cKS5dyra2wOeqXtqDTgJztCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cce63cab3a3707740a69599d76de9c54cb70b250771c276936d4234c55ecc87","last_reissued_at":"2026-05-18T04:41:24.569374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:24.569374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Quartic Kernel for Pathwidth-One Vertex Deletion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Geevarghese Philip, Venkatesh Raman, Yngve Villanger","submitted_at":"2010-09-04T05:39:41Z","abstract_excerpt":"The pathwidth of a graph is a measure of how path-like the graph is. 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