if there are n = 2 vertices in a connected graph, i am supposed to have "n/2 edge disjoint spanning trees". This means i should have 1 edge disjoint spanning tree for a n = 2 graph?
My best guess is that if i remove the only edge between a to b, the connected graph is not disconnected. however, the only result i see from doing this is getting 2 separate disconnected graphs.
please please clarify or define to me what an "edge disjoint spanning tree" means ? When i google the term, I only get a bunch of research papers that I cannot understand.
thank you very much
Best Answer
It just means that you have a set of $n/2$ spanning trees where no two trees in the set have an edge in common. So it is a property of pairs of trees, not a single tree. Thus it is trivially satisfied for the only connected graph on $n=2$ verices.