episciences.org_2078_1653754695
1653754695
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
06
20
2014
Vol. 16 no. 2
PRIMA 2013
A matroid associated with a phylogenetic tree
Andreas
Dress
Katharina
Huber
Mike
Steel
Special issue PRIMA 2013
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 nonnegative 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) Xtree T defined by the requirement that its bases are exactly the \textquotelefttight edgeweight lassos\textquoteright for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T.
06
20
2014
2078
https://hal.archivesouvertes.fr/hal01185618v1
10.46298/dmtcs.2078
https://dmtcs.episciences.org/2078

https://dmtcs.episciences.org/2078/pdf