{"paper":{"title":"Right-angled Artin groups and full subgraphs of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Takuya Katayama","submitted_at":"2016-12-06T10:14:23Z","abstract_excerpt":"For a finite graph $\\Gamma$, let $G(\\Gamma)$ be the right-angled Artin group defined by the complement graph of $\\Gamma$. We show that, for any linear forest $\\Lambda$ and any finite graph $\\Gamma$, $G(\\Lambda)$ can be embedded into $G(\\Gamma)$ if and only if $\\Lambda$ can be realised as a full subgraph of $\\Gamma$. We also prove that if we drop the assumption that $\\Lambda$ is a linear forest, then the above assertion does not hold, namely, for any finite graph $\\Lambda$, which is not a linear forest, there exists a finite graph $\\Gamma$ such that $G(\\Lambda)$ can be embedded into $G(\\Gamma)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01732","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"}