Blocks and cut vertices of the Buneman graph

Dress, A. W. M., Huber, K. T., Koolen, J. and Moulton, V. ORCID: (2011) Blocks and cut vertices of the Buneman graph. SIAM Journal on Discrete Mathematics, 25 (4). pp. 1902-1919.

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Given a set $\Sigma$ of bipartitions of some finite set $X$ of cardinality at least $2$, one can associate to $\Sigma$ a canonical $X$-labeled graph $\mathcal{B}(\Sigma)$, 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 cut vertices of $\mathcal{B}(\Sigma)$, i.e., vertices whose removal disconnect the graph, as well as its blocks or $2$-connected components—results that yield, in particular, an intriguing generalization of the well-known fact that $\mathcal{B}(\Sigma)$ is a tree if and only if any two splits in $\Sigma$ are compatible

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Rhiannon Harvey
Date Deposited: 09 Jan 2012 10:25
Last Modified: 21 Nov 2022 11:30
DOI: 10.1137/090764360

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