{"paper":{"title":"Twin-width of subdivisions of multigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Debsoumya Chakraborti, Jungho Ahn, Kevin Hendrey, Sang-il Oum","submitted_at":"2023-06-08T16:33:28Z","abstract_excerpt":"For each $d\\leq3$, we construct a finite set $F_d$ of multigraphs such that for each graph $H$ of girth at least $5$ obtained from a multigraph $G$ by subdividing each edge at least two times, $H$ has twin-width at most $d$ if and only if $G$ has no minor in $F_d$. This answers a question of Berg\\'{e}, Bonnet, and D\\'{e}pr\\'{e}s asking for the structure of graphs $G$ such that each long subdivision of $G$ has twin-width $4$. As a corollary, we show that the $7\\times7$ grid has twin-width $4$, which answers a question of Schidler and Szeider."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05334","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/2306.05334/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"}