# Edge that is not a light edge in a MST [duplicate]

For a graph $$G$$, consider its minimum spanning tree $$T$$ and let $$e = (a,b)$$ be an edge that is not a light edge for a given cut $$C$$. Then $$e$$ never belongs to $$T$$.
• Try a proof by contradiction. 1) Assume $T$ is an MST in $G$. 2) Assume $e$ is not a light edge for a cut $C$, but that $e$ belongs to $T$. 3) Use (2) to prove that (1) does not hold. 4) Conclude a contradiction, thus (2) is not possible to be true. – ryan Mar 28 at 16:54