{"paper":{"title":"Generating infinite random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csaba Bir\\'o, Udayan B. Darji","submitted_at":"2012-05-14T21:11:44Z","abstract_excerpt":"We define a growing model of random graphs. Given a sequence of nonnegative integers $\\{d_n\\}_{n=0}^\\infty$ with the property that $d_i\\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\\ldots$ by the following process: vertex $v_i$ is connected to a subset of\n  $\\{v_0,\\ldots,v_{i-1}\\}$ of cardinality $d_i$ chosen uniformly at random. We study the resulting probability space. In particular, we give a new characterization of random graph and we also give probabilistic methods for constructing infinite random trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3198","kind":"arxiv","version":6},"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"}