{"paper":{"title":"On the structure of graphs with given odd girth and large minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mathias Schacht, Silvia Messuti","submitted_at":"2016-02-11T21:27:16Z","abstract_excerpt":"We study minimum degree conditions for which a graph with given odd girth has a simple structure. For example, the classical work of Andr\\'asfai, Erd\\H os, and S\\'os implies that every $n$-vertex graph with odd girth $2k+1$ and minimum degree bigger than $\\frac{2}{2k+1}n$ must be bipartite. We consider graphs with a weaker condition on the minimum degree. Generalizing results of H\\\"aggkvist and of H\\\"aggkvist and Jin for the cases $k=2$ and $3$, we show that every $n$-vertex graph with odd girth $2k+1$ and minimum degree bigger than $\\frac{3}{4k}n$ is homomorphic to the cycle of length $2k+1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03904","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"}