On dissimilarity vectors of (not necessarily positive) weighted trees

2010/04/20 by Rubei, Elena
#05C05 #05C12 #92B05 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1004.3406

Abstract

Let T be a (not necessarily positive) weighted tree with n leaves numbered by the set 1,...,n. Define the k-weights of the tree D_i1,....,ik(T) as the sum of the lengths of the edges of the minimal subtree connecting i₁,....,i_k. We will call such numbers "k-weights" of the tree. In this paper, we characterize the sets of real numbers indexed by the subsets of any cardinality >= 2 of a n-set to be the weights of a tree with n leaves.

Related

• A characterization of dissimilarity families of trees
• Buneman's theorem for trees with exatcly n vertices
• A tropical interpretation of m-dissimilarity maps
• Sets of double and triple weights of trees
• On graphlike k-dissimilarity vectors