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Alon, Krivelevich, and Sudokov proved $\\mathbb{E} [\\chi(G_p)] \\geq C_p \\frac{\\chi(G)}{\\log |V(G)|}$, and Bukh conjectured an improvement of $\\mathbb{E}[\\chi(G_p)] \\geq C_p \\frac{\\chi(G)}{\\log \\chi(G)}$. We prove a new spectral lower bound on $\\mathbb{E}[\\chi(G_p)]$, as progress towards Bukh's conjecture. We also propose the stronger conjecture that for any fixed $p \\leq 1/2$, among all graphs of fixed chromatic number, $\\mathbb{E}[\\chi(G_p)]$ is min"},"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":"1811.02018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T20:25:01Z","cross_cats_sorted":[],"title_canon_sha256":"16d4ef66b102fee64d92a6763e9ef19c9de8b5d46de34dc6ded99b98820fe942","abstract_canon_sha256":"205baf9c915453a0921bad1e2498c1cc56ce58bba2d954764e5590755174e0ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:32.550388Z","signature_b64":"PZrlvqY1siZpUIUFdYaQXhKBXHVtL0mwQ9C6iPwpof7xO0G2h9zoShhC6Zg0b6rYy4IZUL+jSv5sTbNJZMz8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9525517ef03253393da81a73e185abcad2c2490d187543ee838f0665d69bcf52","last_reissued_at":"2026-05-18T00:01:32.549926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:32.549926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expected Chromatic Number of Random Subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Lee, David Townley, Henry Reichard, Pat Devlin, Ross Berkowitz","submitted_at":"2018-11-05T20:25:01Z","abstract_excerpt":"Given a graph $G$ and $p \\in [0,1]$, let $G_p$ denote the random subgraph of $G$ obtained by keeping each edge independently with probability $p$. 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