{"paper":{"title":"One-point concentration of the clique and chromatic numbers of the random Cayley graph on F_2^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rudi Mrazovi\\'c","submitted_at":"2015-10-20T18:08:26Z","abstract_excerpt":"Green showed that there exist constants $C_1,C_2>0$ such that the clique number $\\omega$ of the random Cayley graph on $\\mathbb{F}_2^n$ satisfies $\\lim_{n\\to\\infty}\\mathbb{P}(C_1n\\log n < \\omega < C_2n\\log n)=1$. In this paper we find the best possible $C_1$ and $C_2$. Moreover, we prove that for $n$ in a set of density $1$, clique number is actually concentrated on a single value. As a simple consequence of these results, we also prove the one-point concentration result for the chromatic number, thus proving the $\\mathbb{F}_2^n$ analogue of the famous conjecture by Bollob\\'{a}s and giving alm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05991","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"}