{"paper":{"title":"Comments on \"$\\mathcal{O}(m\\cdot n)$ algorithms for the recognition and isomorphism problems on circular-arc graphs\"","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Tomasz Krawczyk","submitted_at":"2024-11-20T20:58:08Z","abstract_excerpt":"In the work [$\\mathcal{O}(m\\cdot n)$ algorithms for the recognition and isomorphism problems on circular-arc graphs, SIAM J. Comput. 24(3), 411--439, (1995)], Wen-Lian Hsu claims three results concerning the class of circular-arc graphs: - the design of so-called \\emph{decomposition trees} that represent the structure of all normalized intersection models of circular-arc graphs, - an $\\mathcal{O}(m\\cdot n)$ recognition algorithm for circular-arc graphs, - an $\\mathcal{O}(m\\cdot n)$ isomorphism algorithm for circular-arc graphs. In [Discrete Math. Theor. Comput. Sci., 15(1), 157--182, 2013] Cur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13708","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/2411.13708/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"}