{"paper":{"title":"Finite subgraphs of an extension graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Juyoung Lee, Sang-hyun Kim, Thomas Koberda","submitted_at":"2017-08-07T12:17:47Z","abstract_excerpt":"Let $\\Gamma$ be a finite graph and let $\\Gamma^{\\mathrm{e}}$ be its extension graph. We inductively define a sequence $\\{\\Gamma_i\\}$ of finite induced subgraphs of $\\Gamma^{\\mathrm{e}}$ through successive applications of an operation called \"doubling along a star\". Then we show that every finite induced subgraph of $\\Gamma^{\\mathrm{e}}$ is isomorphic to an induced subgraph of some $\\Gamma_i$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02088","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":""},"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"}