This paper presents algorithms for computing a minimum 3 ‐way cut and a minimum 4 ‐way cut of an undirected weighted graph G . Let G=(V, E) be an undirected graph with n vertices, m edges, and positive edge weights. Goldschmidt and Hochbaum presented an algorithm for the minimum k ‐way cut problem with fixed k , that requires O(n
4
) and O(n
6
) maximum flow computations, respectively, to compute a minimum 3 ‐way cut and a minimum 4 ‐way cut of G . In this paper we first show some properties on minimum 3 ‐way cuts and minimum 4 ‐way cuts, which indicate a recursive structure of the minimum k ‐way cut problem when k = 3 and 4 . Then, based on those properties, we give divide‐and‐conquer algorithms for computing a minimum 3 ‐way cut and a minimum 4 ‐way cut of G , which require O(n
3
) and O(n
4
) maximum flow computations, respectively.
