A simple proof of a minimum cut algorithm and its applications

For the correctness of the minimum cut algorithm proposed by Nagamochi and Ibaraki, several simple proofs have been presented so far. This paper gives yet another simple proof. As a byproduct, it can provide an O(m log n) time algorithm that outputs a maximum flow between the pair of vertices s and t selected by the algorithm, where n and m are the numbers of vertices and edges, respectively. This algorithm can be used to speed up the algorithm to compute DAGs,t that represents all minimum cuts separating vertices s and t in a graph G, and the algorithm to compute the cactus Γ(G) that represents all minimum cuts in G.