{"paper":{"title":"Directed Ramsey number for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Matija Bucic, Shoham Letzter","submitted_at":"2017-08-15T14:14:50Z","abstract_excerpt":"In this paper, we study Ramsey-type problems for directed graphs. We first consider the $k$-colour oriented Ramsey number of $H$, denoted by $\\overrightarrow{R}(H,k)$, which is the least $n$ for which every $k$-edge-coloured tournament on $n$ vertices contains a monochromatic copy of $H$. We prove that $ \\overrightarrow{R}(T,k) \\le c_k|T|^k$ for any oriented tree $T$. This is a generalisation of a similar result for directed paths by Chv\\'atal and by Gy\\'arf\\'as and Lehel, and answers a question of Yuster. In general, it is tight up to a constant factor.\n  We also consider the $k$-colour direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04504","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"}