2
$\begingroup$

We all know that:

Every graph has an MST. The MST need not be unique, but it is unique if all the edge weights of the graph are distinct.

But if the weights of the edges in a connected graph are not all distinct, does it mean that there is more than one minimum spanning tree?

Yuval Filmus
281k27 gold badges319 silver badges516 bronze badges
asked Jun 13, 2021 at 17:29
$\endgroup$
1
  • 1
    $\begingroup$ not necessarily. For example if your graph is a tree, there is only one MST even if the weights are all the same $\endgroup$ Commented Jun 14, 2021 at 15:48

1 Answer 1

4
$\begingroup$

The MST can be unique even if edge weights repeat. For example, consider the graph on $\{1,\ldots,n\}$ in which the weight of $(1,2),(2,3),\ldots,(n-1,n)$ is 1ドル$ and the weight of all other edges is 2ドル$.

answered Jun 13, 2021 at 17:39
$\endgroup$
1
  • 1
    $\begingroup$ @Toothless, why not accepting the answer by clicking the "checkmark" button underneath the vote buttons? (This comment will be deleted upon feedback.) $\endgroup$ Commented Feb 28, 2022 at 17:21

Your Answer

Draft saved
Draft discarded

Sign up or log in

Sign up using Google
Sign up using Email and Password

Post as a guest

Required, but never shown

Post as a guest

Required, but never shown

By clicking "Post Your Answer", you agree to our terms of service and acknowledge you have read our privacy policy.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.