Skip to Main content Skip to Navigation
Journal articles

A matroid associated with a phylogenetic tree

Abstract : A (pseudo-)metric D on a finite set X is said to be a \textquotelefttree metric\textquoteright if there is a finite tree with leaf set X and non-negative edge weights so that, for all x,y ∈X, D(x,y) is the path distance in the tree between x and y. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is – up to canonical isomorphism – uniquely determined by D, and one does not even need all of the distances in order to fully (re-)construct the tree\textquoterights edge weights in this case. Thus, it seems of some interest to investigate which subsets of X, 2 suffice to determine (\textquoteleftlasso\textquoteright) these edge weights. In this paper, we use the results of a previous paper to discuss the structure of a matroid that can be associated with an (unweighted) X-tree T defined by the requirement that its bases are exactly the \textquotelefttight edge-weight lassos\textquoteright for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T.
Document type :
Journal articles
Complete list of metadata

Cited literature [7 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185618
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 5:14:02 PM
Last modification on : Friday, April 24, 2020 - 2:44:04 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:08:35 AM

File

dmtcs-16-2-4.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185618, version 1

Collections

Citation

Andreas Dress, Katharina Huber, Mike Steel. A matroid associated with a phylogenetic tree. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 2 (in progress) (2), pp.41--55. ⟨hal-01185618⟩

Share

Metrics

Record views

145

Files downloads

920