Dress, A. W. M., Huber, K. T., Koolen, J. and Moulton, V. ORCID: https://orcid.org/0000-0001-9371-6435
(2011)
*Blocks and cut vertices of the Buneman graph.*
SIAM Journal on Discrete Mathematics, 25 (4).
pp. 1902-1919.

## Abstract

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 |
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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 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/35935 |

DOI: | 10.1137/090764360 |

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