{"paper":{"title":"The Twin-Width of Graphs of Bounded VC-Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Sophie Spirkl, Taite LaGrange, Therese Biedl","submitted_at":"2026-06-19T17:48:49Z","abstract_excerpt":"In this paper, we investigate which hereditary classes of graphs admit sub-linear (in the number of vertices) bounds on twin-width. By modifying conference graphs, we can show that split, bipartite, and co-bipartite graphs can all have linear twin-width. However, excluding an induced subgraph of each of these three types is equivalent to the class of graphs having bounded VC-dimension, as shown by Bousquet, Lagoutte, Li, Parreau and Thomass\\'e. Graphs of bounded VC-dimension can have unbounded twin-width, but whether it can be linear was an open question. In this paper, we first present a tool"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21640","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/2606.21640/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"}