0
$\begingroup$

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?

$\endgroup$
3
$\begingroup$

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 $G$.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.