{"paper":{"title":"On the rational Tur\\'an exponents conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dong Yeap Kang, Hong Liu, Jaehoon Kim","submitted_at":"2018-11-16T17:00:15Z","abstract_excerpt":"The extremal number $\\mathrm{ex}(n,F)$ of a graph $F$ is the maximum number of edges in an $n$-vertex graph not containing $F$ as a subgraph. A real number $r \\in [1,2]$ is realisable if there exists a graph $F$ with $\\mathrm{ex}(n , F) = \\Theta(n^r)$. Several decades ago, Erd\\H{o}s and Simonovits conjectured that every rational number in $[1,2]$ is realisable. Despite decades of effort, the only known realisable numbers are $0,1, \\frac{7}{5}, 2$, and the numbers of the form $1+\\frac{1}{m}$, $2-\\frac{1}{m}$, $2-\\frac{2}{m}$ for integers $m \\geq 1$. In particular, it is not even known whether t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06916","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"}