{"paper":{"title":"On the structure of normalized models of circular-arc graphs -- Hsu's approach revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Tomasz Krawczyk","submitted_at":"2024-11-20T14:52:43Z","abstract_excerpt":"Circular-arc graphs are the intersection graphs of arcs of a circle. The main result of this work describes the structure of all \\emph{normalized intersection models} of circular-arc graphs. Normalized models of a circular-arc graph reflect the neighborhood relation between its vertices and can be seen as its canonical representations; in particular, any intersection model can be made normalized by possibly extending some of its arcs. We~devise a data-structure, called \\emph{PQM-tree}, that maintains the set of all normalized models of a circular-arc graph. We show that the PQM-tree of a circu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13374","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/2411.13374/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"}