Thts paper deals wRh the problem of enumerating all the cutsets or all the s-t cutsets separatmg two spectfied verttces s and t m an undirected graph A vanety of approaches have been proposed for this problem, among which one based on the partmon era set of veruces rote two sets is the most effi¢ienL It is first shown that an algorithm of this type has time complexity O((n + m)(n -log2#)#), and two new algorithms with ume complexity O((n + m)O + I)) are then proposed One of these new algorithms has space complexity O(nZ), and the other has space complexity O(n + m), where n and m are the numbers of veraces and edges, respectively, and ta ts the number ofs-t cutsets m a given graph The results of some computatmnal experiments are also described.An mvest~gaUon ~s made of the extent to whtch the new algorithms are better, and how good the performance of the old algorithm is, especmlly when a given graph is "dense," t e, 2m/(n(n -1)) _> 0.4.

The problem of generating all the maximal independent sets (or maximal cliques) of a given graph is fundamental in graph theory and is also one of the most important in terms of the application of graph theory. In this paper, we present a new efficient algorithm for generating all the maximal independent sets, for which processing time and memory space are bounded by $O(nm\mu)$ and $O(n+m)$, respectively, where n, m, and $\mu$ are the numbers of vertices, edges, and maximal independent sets of a graph.