I need help in finding a solution to this problem and answering my questions:
first: is there any particular name for this problem?
second: how can we solve it?
third: it is not always possible to find such an orientation of the edges depending on the graph: what are the constraints to be satisfied?
and at last, is it a polynomial problem?
Objective: assign directions and colors(red and green) to the edges of the graph $G(V,E)$ such that for every pair of nodes $v$ and $v’$, there is a at least one green colored path and one red-colored path from $v$ to $v’$ and at least one green colored path and one red colored path path from $v’$ to $v$.