{"paper":{"title":"Induced Minors, Asymptotic Dimension, and Baker's Technique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.GR","math.GT","math.MG"],"primary_cat":"math.CO","authors_text":"Robert Hickingbotham","submitted_at":"2025-08-08T10:12:03Z","abstract_excerpt":"Asymptotic dimension is a large-scale invariant of metric spaces that was introduced by Gromov (1993). We prove that every hereditary class of bounded-degree graphs that excludes some graph as a fat minor has asymptotic dimension at most $2$, which is optimal. This makes substantial progress on a question of Bonamy, Bousquet, Esperet, Groenland, Liu, Pirot, and Scott (J. Eur. Math. Soc. 2023).\n  The key to our proof is a notion inspired by Baker's technique (J. ACM 1994). We say that a graph class $\\mathcal{G}$ has bounded Baker-treewidth if there exists a function $f \\colon \\mathbb{N} \\to \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.06190","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/2508.06190/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"}