{"paper":{"title":"Kneser ranks of random graphs and minimum difference representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ida Kantor, Zolt\\'an F\\\"uredi","submitted_at":"2017-01-28T14:18:12Z","abstract_excerpt":"Every graph $G=(V,E)$ is an induced subgraph of some Kneser graph of rank $k$, i.e., there is an assignment of (distinct) $k$-sets $v \\mapsto A_v$ to the vertices $v\\in V$ such that $A_u$ and $A_v$ are disjoint if and only if $uv\\in E$. The smallest such $k$ is called the Kneser rank of $G$ and denoted by $f_{\\rm Kneser}(G)$. As an application of a result of Frieze and Reed concerning the clique cover number of random graphs we show that for constant $0< p< 1$ there exist constants $c_i=c_i(p)>0$, $i=1,2$ such that with high probability \\[ c_1 n/(\\log n)< f_{\\rm Kneser}(G) < c_2 n/(\\log n). \\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08292","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"}