{"paper":{"title":"On graph-restrictive permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Gabriel Verret, Pablo Spiga, Primoz Potocnik","submitted_at":"2011-01-27T00:22:39Z","abstract_excerpt":"Let $\\Gamma$ be a connected $G$-vertex-transitive graph, let $v$ be a vertex of $\\Gamma$ and let $L=G_v^{\\Gamma(v)}$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\\Gamma(v)$. Then $(\\Gamma,G)$ is said to be \\emph{locally-$L$}. A transitive permutation group $L$ is \\emph{graph-restrictive} if there exists a constant $c(L)$ such that, for every locally-$L$ pair $(\\Gamma,G)$ and an arc $(u,v)$ of $\\Gamma$, the inequality $|G_{uv}|\\leq c(L)$ holds.\n  Using this terminology, the Weiss Conjecture says that primitive groups are graph-restrictive. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5186","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"}