Abstract
One wishes to remove k--1 edges of a vertex-weighted tree T such that the weightsof the k induced connected components are approximately the same. How well canone do it? In this paper, we investigate such k-separators for quasi-binary trees. Weshow 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) weightedcomponent is lower (respectively upper) bounded. Examples showing optimality forthe lower bound are also given.