{"paper":{"title":"Odd cycles in subgraphs of sparse pseudorandom graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joonkyung Lee, Mathias Schacht, S\\\"oren Berger","submitted_at":"2019-06-12T12:55:45Z","abstract_excerpt":"We answer two extremal questions about odd cycles that naturally arise in the study of sparse pseudorandom graphs. Let $\\Gamma$ be an $(n,d,\\lambda)$-graph, i.e., $n$-vertex, $d$-regular graphs with all nontrivial eigenvalues in the interval $[-\\lambda,\\lambda]$. Krivelevich, Lee, and Sudakov conjectured that, whenever $\\lambda^{2k-1}\\ll d^{2k}/n$, every subgraph $G$ of $\\Gamma$ with $(1/2+o(1))e(\\Gamma)$ edges contains an odd cycle $C_{2k+1}$. Aigner-Horev, H\\`{a}n, and the third author proved a weaker statement by allowing an extra polylogarithmic factor in the assumption $\\lambda^{2k-1}\\ll "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05100","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"}