{"paper":{"title":"Problems related to strong connectivity and strong biconnectivity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Raed Jaberi","submitted_at":"2026-06-15T00:56:38Z","abstract_excerpt":"Let $G=(V,E)$ be a strong biconnected graph and let $B \\subseteq V$ such that for each vertex $w \\in B$, the subgraph $G \\setminus \\lbrace w\\rbrace$ is strongly connected. In this paper we study the problem of computing a subset $E_{\\beta} \\subseteq E$ of minimum size such that the subgraph $G_{\\beta}=(V,E_{\\beta})$ is strongly biconnected and for each vertex $w \\in B$, the subgraph $G_{\\beta} \\setminus \\lbrace w\\rbrace$ is strongly connected. We prove that there exists a polynomial time $7$-approximation algorithm for this problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16087","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/2606.16087/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"}