Characterizing the flow equivalent trees of a network Original Research Article

Consider a connected graph G with positive edge capacities. Gomory and Hu (J. SIAM 9 (1961) 551) showed that there always exists a tree T with positive edge capacities, on the same node set as G, such that the max flow value between any pair of nodes in G is the same as the max flow value between the corresponding pair of nodes in T. Such a tree is called a flow equivalent tree for G and need not be unique. In this paper, we present a “compact” (i.e., polynomial size) characterization of the collection of all flow equivalent trees for a graph G. We also present a polynomial time algorithm for recognizing such representations.