# To Prove G/e is acyclic

Let G be an acyclic graph and let e $\in$ E, Show that G/e is acyclic. Where "/" means contract in graph theory.

How can I write an intuitive proof?

Let $v$ be the vertex resulting from the merger of the endpoints $u$ and $w$ of $e$. Suppose that $G/e$ has a cycle $C$.
• Show that if $v$ is not in $C$, then $C$ is a cycle in $G$.
• Show that if $v$ is in $C$, then replacing it with $u$ and $w$ in one order or the other yields a cycle in $G$.