Now given a set of cells that includes the root, we want to search for transport systems, with the root cell as the root of the graph, which have minimal cost.

It is easy to see that in general there will be many possible transport systems for a given collection of cells. All we have to do is note that there can be a main vein starting at the root, with major branches coming off the main vein. Since there are many choices for the path of the main vein, this already shows the existence of multiple transport systems.