{"paper":{"title":"Infinite primitive directed graphs","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Simon Smith","submitted_at":"2006-02-01T11:19:10Z","abstract_excerpt":"A group $G$ of permutations of a set $\\Omega$ is {\\em primitive} if it acts transitively on $\\Omega$, and the only $G$-invariant equivalence relations on $\\Omega$ are the trivial and universal relations. A graph $\\Gamma$ is {\\em primitive} if its automorphism group acts primitively on its vertex set.\n  A graph $\\Gamma$ has {\\em connectivity one} if it is connected and there exists a vertex $\\alpha$ of $\\Gamma$, such that the induced graph $\\Gamma \\setminus \\{\\alpha\\}$ is not connected. If $\\Gamma$ has connectivity one, a {\\em block} of $\\Gamma$ is a connected subgraph that is maximal subject t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602011","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"}