{"paper":{"title":"A Note on the Rainbow Connectivity of Tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jes\\'us Alva-Samos, Juan Jos\\'e Montellano-Ballesteros","submitted_at":"2015-04-27T15:51:21Z","abstract_excerpt":"An arc-coloured digraph $D$ is said to be \\emph{rainbow connected} if for every two vertices $u$ and $v$ there is an $uv$-path all whose arcs have different colours. The minimun number of colours required to make the digraph rainbow connected is called the \\emph{rainbow connection number} of $D$, denoted $\\stackrel{\\rightarrow}{rc}(D)$. In \\cite{Dorbec} it was showed that if $T$ is a strong tournament with $n\\geq 5$ vertices, then $2\\leq \\stackrel{\\rightarrow}{rc}(T)\\leq n-1$; and that for every $n$ and $k$ such that $3\\leq k\\leq n-1$, there exists a tournament $T$ on $n$ vertices such that $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07140","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"}