Transportation polytopes and its relation to graph theory

الملخص EN

Transportation polytopes of non- negative m × n matrices compose of two vectors: a and b which row sums are equal to fixed constant and column sums are equal to different constant.

The transportation polytopes are denoted by T (a, b) and these two vectors are called margins.

An open problem that the 2-way transportation polytopes are Hamiltonian is proved in this paper with application of optimization.