Let $G$ be a graph with $2$ spanning trees.

Question

Question) Let $G$ be a graph with $2$ spanning trees.

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Now we try $K_4$

Now I'm just trying to find if any two trees can be disjoint

tree1:

managed to find two after writing them all down. Therefore the least number of edge-disjoint spanning trees is a graph of $4$ vertices.

Is this right?

Is there an easier way to show this? Mainly had trouble finding all the disjoint spanning trees

Answer 1

That should be totally fine. You checked all possibilities. Actually this is the easiest method in my opinion, but if someone knows an even easier one, I'd be interested in it.