Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 8 / b / ii

True. Delete $e\in T$; the resulting two connected components define a cut of a graph. If a crossing edge $f$ had $w(f)<w(e)$, the exchange $T-e+f$ would be a spanning tree of smaller total weight, contradicting the minimum spanning tree assumption. Thus $e$ is a light edge crossing a cut for this fundamental cut. It need not be uniquely light.