On extreme faces of projective point configurations
Résumé
One wishes to remove k--1 edges of a vertex-weighted tree T such that the weights of the k induced connected components are approximately the same. How well can one do it? In this paper, we investigate such k-separators for quasi-binary trees. We show that, under certain conditions on the total weight of the tree, a particular k- separator can be constructed such that the smallest (respectively the largest) weighted component is lower (respectively upper) bounded. Examples showing optimality for the lower bound are also given.