Abstract. We present an algorithm for finding the minimum cut of an undirected edge-weighted

graph. It is simple in every respect. It has a short and compact descr iption, is easy to implement, and

has a surprisingly simple proof of correctness. Its runtime matches that of the fastest algorithm

known. The runtime analysis is straightforward. In contrast to nearly all approaches so far, the

algorithm uses no flow techniques. Roughly speaking, the algorithm consists of about uVu nearly

identical phases each of which is a maximum adjacency search.