Treelike families of multiweights

2014/04/27 by Baldisserri, Agnese, Rubei, Elena
#05C05 #05C12 #05C22 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.6799

Abstract

Let \cal T=(T,w) be a weighted finite tree with leaves 1,..., n. For any I :=\i₁,..., i_k \ ⊂ \1,...,n\, let D_I (\cal T) be the weight of the minimal subtree of T connecting i₁,..., i_k; the D_I (\cal T) are called k-weights of \cal T. Given a family of real numbers parametrized by the k-subsets of \1,..., n\, \D_I\_I ∈ \1,...,n\ \choose k, we say that a weighted tree \cal T=(T,w) with leaves 1,..., n realizes the family if D_I(\cal T)=D_I for any I . We give a characterization of the families of real numbers that are realized by some weighted tree.

Related

• Families of multiweights and pseudostars
• A characterization of dissimilarity families of trees
• Graphlike families of multiweights
• On dissimilarity vectors of (not necessarily positive) weighted trees
• Sets of double and triple weights of trees