It is well-known that the Ford-Fulkerson algorithm for finding a maximum flow in a network need not terminate if we allow the arc capacities to take irrational values. Every non-terminating example converges to a limit flow, but this limit flow need not be a maximum flow. Hence, one may pass to the limit and begin the algorithm again. In this way, we may view the Ford-Fulkerson algorithm as a t...

This paper considers two similar graph algorithms that work by repeatedly increasing “flow” along “augmenting paths”: the Ford-Fulkerson algorithm for the maximum flow problem and the Gale-Shapley algorithm for the stable allocation problem (a many-to-many generalization of the stable matching problem). Both algorithms clearly terminate when given integral input data. For real-valued input data...

In early 70s Berge conjectured that any bridgeless cubic graph contains five perfect matchings such that each edge belongs to at least one of them. In 1972 Fulkerson conjectured that, in fact, we can find six perfect matchings containing each edge exactly twice. By introducing the concept of an r-graph (a remarkable generalization of one of bridgeless cubic graph) Seymour in 1979 conjectured th...

The maximum flow problem is one of the most fundamental problems in network flow theory and has been investigated extensively. The Ford-Fulkerson algorithm is a simple algorithm to solve the maximum flow problem based on the idea of augmenting path. But its time complexity is high and it’s a pseudo-polynomial time algorithm. In this paper, a parallel Ford-Fulkerson algorithm is given. The idea ...

This paper reviews George Dantzig’s contribution to integer programming, especially his seminal work with Fulkerson and Johnson on the traveling salesman problem.