Flows

Abstract

In this chapter, we look at ‘flows’ in networks: How much can be transported in a network from some ‘source’ s to some ‘sink’ t if the ‘capacities’ of the connections are given? Such a network might be a model for a system of pipelines or a water supply system or for a system of roads. The theory of flows is one of the most important parts of Combinatorial Optimization; it has various applications as well in Mathematics as in other fields. The book by Ford and Fulkerson (1962) ‘Flows in Networks’, formerly the standard reference, is still worth reading; an extensive treatment is in the recent monograph by Ahuja, Magnanti and Orlin (1993). In Chapter 7, we will see several applications of the theory of flows within Combinatorics, and flows and related notions will appear again and again during the remainder of this book.