Edge separators for quasi-binary trees

One wishes to remove k−1k−1 edges of a vertex-weighted tree TT such that the weights of the kk induced connected components are approximately the same. How well can one do it? In this paper, we investigate such kk-separators for quasi-binary   trees. We show that, under certain conditions on the total weight of the tree, a particular kk-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.