Abstract
A (pseudo)metric D on a finite set X is said to be a `tree metric' 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 13; up to canonical isomorphism 13; uniquely determined by D, and one does not even need all of the distances in order to fully (re)construct the tree's edge weights in this case. Thus, it seems of some interest to investigate which subsets of X, 2 suffice to determine (`lasso') 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 `tight edgeweight lassos' for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T.
Original language  English 

Pages (fromto)  4156 
Number of pages  16 
Journal  Discrete Mathematics and Theoretical Computer Science 
Volume  16 
Issue number  2 
Publication status  Published  2014 
Keywords
 phylogenetic tree
 tree metric
 matroid
 lasso (for a tree)
 cord (of a lasso)
Profiles

Katharina Huber
 School of Computing Sciences  Associate Professor
 Computational Biology  Member
Person: Research Group Member, Academic, Teaching & Research