{"paper":{"title":"Tur\\'an's problem and Ramsey numbers for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lin-Lin Wang, Yi-Li Wu, Zhi-Hong Sun","submitted_at":"2011-10-12T18:12:56Z","abstract_excerpt":"Let $T_n^1=(V,E_1)$ and $T_n^2=(V,E_2)$ be the trees on $n$ vertices with $V=\\{v_0,v_1,\\ldots,v_{n-1}\\}$, $E_1=\\{v_0v_1,\\ldots,v_0v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}\\}$, and $E_2=\\{v_0v_1,\\ldots,$ $v_0v_{n-3},v_{n-3}v_{n-2}, v_{n-3}v_{n-1}\\}$. In this paper, for $p\\ge n\\ge 5$ we obtain explicit formulas for $\\ex(p;T_n^1)$ and $\\ex(p;T_n^2)$, where $\\ex(p;L)$ denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a subgraph. Let $r(G\\sb 1, G\\sb 2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. In this paper we also obtain some explicit formulas for $r(T_m,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2725","kind":"arxiv","version":4},"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"}