{"paper":{"title":"Sub-tree counts on hyperbolic random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GT"],"primary_cat":"math.PR","authors_text":"D. Yogeshwaran, Takashi Owada","submitted_at":"2018-02-16T20:11:03Z","abstract_excerpt":"We study the hyperbolic random geometric graph introduced in Krioukov et al. For a sequence $R_n \\to \\infty$, we define these graphs to have the vertex set as Poisson points distributed uniformly in balls $B(0,R_n) \\subset B_d^{\\alpha}$, the $d$-dimensional Poincar\\'e ball (unit d-ball with the Poincar\\'e metric $d_{\\alpha}$ corresponding to negative curvature $-\\alpha^2, \\alpha > 0$) by connecting any two points within a distance $R_n$ according to the metric $d_{\\zeta}, \\zeta > 0$. Denoting these graphs by $HG_n(R_n ; \\alpha, \\zeta)$, we study asymptotic counts of copies of a fixed tree $\\Ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06105","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"}