{"paper":{"title":"On the local density problem for graphs of given odd-girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Reiher, Guilherme Oliveira Mota, Mathias Schacht, Wiebke Bedenknecht","submitted_at":"2016-09-19T13:25:33Z","abstract_excerpt":"Erd\\H{o}s conjectured that every $n$-vertex triangle-free graph contains a subset of $\\lfloor n/2\\rfloor$ vertices that spans at most $n^2/50$ edges. Extending a recent result of Norin and Yepremyan, we confirm this conjecture for graphs homomorphic to so-called Andr\\'asfai graphs. As a consequence, Erd\\H{o}s' conjecture holds for every triangle-free graph $G$ with minimum degree $\\delta (G)>10n/29$ and if $\\chi (G)\\leq 3$ the degree condition can be relaxed to $\\delta (G)> n/3$. In fact, we obtain a more general result for graphs of higher odd-girth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05712","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"}