Do any two spanning trees of a simple graph always have some common edges?

I tried few cases and found any two spanning tree of a simple graph has some common edges. I mean I couldn’t find any counter example so far. But I couldn’t prove or disprove this either. How to prove or disprove this conjecture?


No, consider the complete graph K4:

It has the following edge-disjoint spanning trees:
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Source : Link , Question Author : Mr. Sigma. , Answer Author : Bjørn Kjos-Hanssen

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