Maximal Flow Through a Network

@article{Ford1956MaximalFT,
  title={Maximal Flow Through a Network},
  author={Lester Randolph Ford and Delbert Ray Fulkerson},
  journal={Canadian Journal of Mathematics},
  year={1956},
  volume={8},
  pages={399 - 404}
}
Introduction. The problem discussed in this paper was formulated by T. Harris as follows: “Consider a rail network connecting two cities by way of a number of intermediate cities, where each link of the network has a number assigned to it representing its capacity. Assuming a steady state condition, find a maximal flow from one given city to the other.” 

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References

SHOWING 1-2 OF 2 REFERENCES

Non-Separable and Planar Graphs.

  • H. Whitney
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1931
A dual of a graph is defined by combinatorial means, and the paper ends with the theorem that a necessary and sufficient condition that a graph be planar is that it have a dual.

Maximization of a linear function of variables subject to linear inequalities: Activity analysis of production and allocation (Cowles Commission

  • Maximization of a linear function of variables subject to linear inequalities: Activity analysis of production and allocation (Cowles Commission
  • 1951