{"paper":{"title":"On the Max-Cut of Sparse Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Gamarnik, Quan Li","submitted_at":"2014-11-06T18:42:41Z","abstract_excerpt":"We consider the problem of estimating the size of a maximum cut (Max-Cut problem) in a random Erd\\H{o}s-R\\'{e}nyi graph on $n$ nodes and $\\lfloor cn \\rfloor$ edges. It is shown in Coppersmith et al. ~\\cite{Coppersmith2004} that the size of the maximum cut in this graph normalized by the number of nodes belongs to the asymptotic region $[c/2+0.37613\\sqrt{c},c/2+0.58870\\sqrt{c}]$ with high probability (w.h.p.) as $n$ increases, for all sufficiently large $c$.\n  In this paper we improve both upper and lower bounds by introducing a novel bounding technique. Specifically, we establish that the size"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1698","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"}