{"paper":{"title":"Equivalence between pathbreadth and strong pathbreadth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Arne Leitert, Guillaume Ducoffe","submitted_at":"2018-09-17T06:40:31Z","abstract_excerpt":"We say that a given graph $G = (V, E)$ has \\emph{pathbreadth} at most $\\rho$, denoted $\\pb(G) \\leq \\rho$, if there exists a Roberston and Seymour's path decomposition where every bag is contained in the $\\rho$-neighbourhood of some vertex. Similarly, we say that $G$ has \\emph{strong pathbreadth} at most $\\rho$, denoted $\\spb(G) \\leq \\rho$, if there exists a Roberston and Seymour's path decomposition where every bag is the complete $\\rho$-neighbourhood of some vertex. It is straightforward that $\\pb(G) \\leq \\spb(G)$ for any graph $G$. Inspired from a close conjecture in [Leitert and Dragan, COC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06041","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":""},"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"}