{"paper":{"title":"Ramsey numbers for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhi-Hong Sun","submitted_at":"2011-03-14T15:07:18Z","abstract_excerpt":"For $n\\ge 5$ let $T_n'$ denote the unique tree on $n$ vertices with $\\Delta(T_n')=n-2$, and let $T_n^*=(V,E)$ be the tree on $n$ vertices with $V=\\{v_0,v_1,\\ldots,$ $v_{n-1}\\}$ and $E=\\{v_0v_1,\\ldots,v_0v_{n-3},$ $v_{n-3}v_{n-2},v_{n-2}v_{n-1}\\}$. In this paper we evaluate the Ramsey numbers $r(G_m,T_n')$ and $r(G_m,T_n^*)$, where $G_m$ is a connected graph of order $m$. As examples, for $n\\ge 8$ we have $r(T_n',T_n^*)=r(T_n^*,T_n^*)=2n-5$, for $n>m\\ge 7$ we have $r(K_{1,m-1},T_n^*)=m+n-3$ or $m+n-4$ according as $m-1\\mid (n-3)$ or $m-1\\nmid (n-3)$, for $m\\ge 7$ and $n\\ge (m-3)^2+2$ we have $r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2685","kind":"arxiv","version":6},"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"}