{"paper":{"title":"On the unavoidability of oriented trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fran\\c{c}ois Dross, Fr\\'ed\\'eric Havet","submitted_at":"2018-12-12T21:41:13Z","abstract_excerpt":"A digraph is {\\it $n$-unavoidable} if it is contained in every tournament of order $n$. We first prove that every arborescence of order $n$ with $k$ leaves is $(n+k-1)$-unavoidable. We then prove that every oriented tree of order $n$ ($n\\geq 2$) with $k$ leaves is $(\\frac{3}{2}n+\\frac{3}{2}k -2)$-unavoidable and $(\\frac{9}{2}n -\\frac{5}{2}k -\\frac{9}{2})$-unavoidable, and thus $(\\frac{21}{8} n- \\frac{47}{16})$-unavoidable. Finally, we prove that every oriented tree of order $n$ with $k$ leaves is $(n+ 144k^2 - 280k + 124)$-unavoidable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05167","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"}