The main challenge here lies in devising a mathematically acceptable proof of this impossibility, which is where the foundations for what we today know as graph theory.

We develop a new approach to solving minimum-cost circulation problems. Our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost ...

Thomas E. Dilts, Peter J. Weisberg, Philip Leitner, Marjorie D. Matocq, Richard D. Inman, Kenneth E. Nussear, Todd C. Esque, Multiscale connectivity and graph theory ...