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 $G$.

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