{"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 $p$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02018","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"}