{"paper":{"title":"Buneman's theorem for trees with exatcly n vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agnese Baldisserri","submitted_at":"2014-06-30T20:27:42Z","abstract_excerpt":"Let ${\\cal T}=(T,w)$ be a positive-weighted tree with at least $n$ vertices. For any $i,j \\in \\{1,...,n\\}$, let $D_{i,j} ({\\cal T})$ be the weight of the unique path in $T$ connecting $i$ and $j$. The $D_{i,j} ({\\cal T})$ are called $2$-weights of ${\\cal T}$ and, if we put in order the $2$-weights, the vector which has the $D_{i,j} ({\\cal T})$ as components is called \\emph{$2$-dissimilarity vector} of $ {\\cal T}$. Given a family of positive real numbers $\\{D_{i,j}\\}_{i,j \\in \\{1,...,n\\}}$, we say that a positive-weighted tree ${\\cal T}=(T,w)$ realizes the family if $\\{1,...,n\\} \\subset V(T)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0048","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"}