{"paper":{"title":"Blocks and Cut Vertices of the Buneman Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.W.W. Dress, J. Koolen, K.T. Huber, V. Moulton","submitted_at":"2011-01-25T20:49:54Z","abstract_excerpt":"Given a set $\\Sg$ of bipartitions of some finite set $X$ of cardinality at least 2, one can associate to $\\Sg$ a canonical $X$-labeled graph $\\B(\\Sg)$, called the Buneman graph. This graph has several interesting mathematical properties - for example, it is a median network and therefore an isometric subgraph of a hypercube. It is commonly used as a tool in studies of DNA sequences gathered from populations. In this paper, we present some results concerning the {\\em cut vertices} of $\\B(\\Sg)$, i.e., vertices whose removal disconnect the graph, as well as its {\\em blocks} or 2-{\\em connected co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4927","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"}