{"paper":{"title":"The isoperimetric constant of the random graph process","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Eyal Lubetzky, Itai Benjamini, Michael Krivelevich, Simi Haber","submitted_at":"2005-09-01T15:55:13Z","abstract_excerpt":"The isoperimetric constant of a graph $G$ on $n$ vertices, $i(G)$, is the minimum of $\\frac{|\\partial S|}{|S|}$, taken over all nonempty subsets $S\\subset V(G)$ of size at most $n/2$, where $\\partial S$ denotes the set of edges with precisely one end in $S$. A random graph process on $n$ vertices, $\\widetilde{G}(t)$, is a sequence of $\\binom{n}{2}$ graphs, where $\\widetilde{G}(0)$ is the edgeless graph on $n$ vertices, and $\\widetilde{G}(t)$ is the result of adding an edge to $\\widetilde{G}(t-1)$, uniformly distributed over all the missing edges. We show that in almost every graph process $i(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509022","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0509022/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}