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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). \\]"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.08292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-28T14:18:12Z","cross_cats_sorted":[],"title_canon_sha256":"398f4a0526be14cb2565ff1c5d6d1798dc2f5043777cd0c9149e276025eaf4e2","abstract_canon_sha256":"b3d281c2f2c5aeb2c6678ef2e0b1d7317008a2da8ad59bd6cb583677358c8a8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:54.637079Z","signature_b64":"vCNu+EqtaYPXckSNA0NiNOLrUJSi+ddppQhBvzKxsl3Z/lHJhOH1ZALZV7sJ3gFJVSRw4v3Le3ymAmjfQ5/JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eb3ee2e96bc848dfb7b6ac9bca0a0de35a417778c93fe7b12057cee01d8e852","last_reissued_at":"2026-05-18T00:51:54.636406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:54.636406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $uv\\in E$. 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