Set of edges is MST?

Question

Given a Graph $G = (V,E)$ and given a subset $ T \subset E$. I would like to test, whether T is already a MST of G or not in constant time.

Note: If $T^{MST}$ is the MST of G, then we know that $T \subset T^{MST}.$

I can think of approaches in linear time, but I cannot come up with anything in linear time.

Is there maybe a way to figure out beforehand, how many edges are contained in the MST of G?

Thanks in advance!

Answer 1

The number of edges in a spanning tree of a graph $G$ is one less than the number of vertices of $G$.