{"paper":{"title":"Twin-width one","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Amadeus Reinald, Christophe Paul, Hugo Jacob, Jungho Ahn, Noleen K\\\"ohler, Sebastian Wiederrecht","submitted_at":"2025-01-02T00:56:11Z","abstract_excerpt":"We investigate the structure of graphs of twin-width at most $1$, and obtain the following results:\n  - Graphs of twin-width at most $1$ are permutation graphs. In particular they have an intersection model and a linear structure.\n  - There is always a $1$-contraction sequence closely following a given permutation diagram.\n  - Based on a recursive decomposition theorem, we obtain a simple algorithm running in linear time that produces a $1$-contraction sequence of a graph, or guarantees that it has twin-width more than $1$.\n  - We characterise distance-hereditary graphs based on their twin-wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00991","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.00991/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"}