Tree partitioning via vertex deletion

Motivated by tree partitioning problems, we introduce the notion of i-divider of a tree, t-dividers generalize concepts well-known in literature, such as centroids and separators, that are the backbone of tree decomposition algorithms based on vertex deletion. We characterize the structure of the set of t-dividers of a tree and we present an efficient algorithm for finding t-dividers that is able to avoid visiting the entire tree