{"paper":{"title":"An Improved Error Term for Tur$\\acute{\\rm a}$n Number of Expanded Non-degenerate 2-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guiying Yan, Xin Xu, Yucong Tang","submitted_at":"2019-03-30T04:22:36Z","abstract_excerpt":"For a 2-graph $F$, let $H_F^{(r)}$ be the $r$-graph obtained from $F$ by enlarging each edge with a new set of $r-2$ vertices. We show that if $\\chi(F)=\\ell>r \\geq 2$, then $ {\\rm ex}(n,H_F^{(r)})= t_r (n,\\ell-1)+ \\Theta( {\\rm biex}(n,F)n^{r-2}),$ where $t_r (n,\\ell-1)$ is the number of edges of an $n$-vertex complete balanced $\\ell-1$ partite $r$-graph and ${\\rm biex}(n,F)$ is the extremal number of the decomposition family of $F$. Since ${\\rm biex}(n,F)=O(n^{2-\\gamma})$ for some $\\gamma>0$, this improves on the bound ${\\rm ex}(n,H_F^{(r)})= t_r (n,\\ell-1)+ o(n^r)$ by Mubayi (2016). Furthermo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00146","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"}