I have a graph where I am trying to find minimum spanning tree using the red rule, blue rule approach.
Now the graph is a directed graph and it has a zero cost cycle near the terminal point. In fact the only arcs to the terminal point come from points on the cycle and they have the same weight. My intuition is that the entire cycle and both arcs will be blue, but I am having trouble making cuts that do not intersect other blue arcs.
Is the red rule, blue rule algorithm useable for a directed graph of this nature?
Can the entire cycle and both arcs to the terminal node be blue?
If not, does the order I make cuts and cycles change which arcs are blue and which are red? (and does that make any sense?)