Cut Star of an Undirected Graph

Abstract

Suppose that [Formula: see text] is an undirected graph. An ordered pair [Formula: see text] of the vertices of the graph [Formula: see text] is called a pendant pair for the graph if [Formula: see text] is a minimum cut separating [Formula: see text] and [Formula: see text] Stoer and Wagner obtained a global minimum cut of [Formula: see text] by using pendant pairs of [Formula: see text] and its contractions. A Gomory Hu tree of the graph [Formula: see text] is a very useful data structure which gives us all the minimum s-t cuts of [Formula: see text] for every pair of distinct vertices [Formula: see text] and [Formula: see text] In this paper, we construct a new type of tree for the graph [Formula: see text] called cut star, by using pendant pairs of [Formula: see text] and its contractions. A cut star of the graph [Formula: see text] is constructed more quickly than a Gomory Hu tree of [Formula: see text] We characterize a class of graphs for which a cut star of a graph of this class is also a Gomory Hu tree.