In minimum spanning trees, the cut property states that if you have a subset of vertices in a graph and there exists an edge that's the smallest in the graph and you have exactly one endpoint for that edge then there exists a MST that contains that edge.
So what if I have a graph that looks like this:
Now the cut does have only one endpoint for the minimum edge but not all the minimum edges will be on that graph. You could also say that there's technically two minimum edges on that end point but then there's no way you can make a cut such that only one minimum end point exists. So is there a way to modify the cut property so that a graph like this could have a cut as shown above and it will still be true?