{"paper":{"title":"Extremal results for odd cycles in sparse pseudorandom graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elad Aigner-Horev, Hiep H\\`an, Mathias Schacht","submitted_at":"2016-02-11T10:18:34Z","abstract_excerpt":"We consider extremal problems for subgraphs of pseudorandom graphs. For graphs $F$ and $\\Gamma$ the generalized Tur\\'an density $\\pi_F(\\Gamma)$ denotes the density of a maximum subgraph of $\\Gamma$, which contains no copy of~$F$. Extending classical Tur\\'an type results for odd cycles, we show that $\\pi_{F}(\\Gamma)=1/2$ provided $F$ is an odd cycle and $\\Gamma$ is a sufficiently pseudorandom graph. In particular, for $(n,d,\\lambda)$-graphs $\\Gamma$, i.e., $n$-vertex, $d$-regular graphs with all non-trivial eigenvalues in the interval $[-\\lambda,\\lambda]$, our result holds for odd cycles of len"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03663","kind":"arxiv","version":2},"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"}