{"paper":{"title":"Embeddability of right-angled Artin groups on complements of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eon-Kyung Lee, Sang-Jin Lee","submitted_at":"2017-06-30T02:15:04Z","abstract_excerpt":"For a finite simplicial graph $\\Gamma$, let $A(\\Gamma)$ denote the right-angled Artin group on $\\Gamma$. Recently Kim and Koberda introduced the extension graph $\\Gamma^e$ for $\\Gamma$, and established the Extension Graph Theorem: for finite simplicial graphs $\\Gamma_1$ and $\\Gamma_2$ if $\\Gamma_1$ embeds into $\\Gamma_2^e$ as an induced subgraph then $A(\\Gamma_1)$ embeds into $A(\\Gamma_2)$. In this article we show that the converse of this theorem does not hold for the case $\\Gamma_1$ is the complement of a tree and for the case $\\Gamma_2$ is the complement of a path graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10002","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":""},"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"}