The number of spanning trees in a simple graph with no cut edges

Question

Let $t(G)$ be the number of spanning trees in a graph $G$. Leg $e(G)$ be the number of edges in a graph $G$.

For $G$ a simple graph with no cut edges yields: $t(G) \geq e(G)$

I believe it is true, but I can't make it explicit.

I already know when equality holds: when the graph is cyclic.

Answer 1

For any edge $e$, $t(G)=t(G-e)+t(G/e)$ where $G-e$ is the graph obtained by deleting $e$ and $G/e$ is the graph obtained by contracting $e$. Apply induction on $m$.