Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Considering loop free cubic graphs (graphs where every node has 3 neighboring nodes): Is is possible to construct a spanning tree that only has nodes with 3 neighbors in the spanning tree or 1 neighbor in the spanning tree (leaves).

That is I want to be able to construct a spanning tree where there are no nodes that are connected to only 2 other nodes in the spanning tree. They should all be connected to either 1 node (a leaf) or all their edges in the underlying cubic graph should also be present in the spanning tree (ie attached to 3 nodes in the spanning tree)?

Does anyone know the answer to this? And if it is possible, how to construct such a spanning tree? Many thanks.

share|improve this question

1 Answer 1

It's not always possible. For example:

Counter-example

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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