#### Title

Full Degree Spanning Trees in Random Cubic Graphs

#### Presentation Type

Poster

#### Faculty Advisor

Deepak Bal

#### Access Type

Event

#### Start Date

26-4-2023 11:00 AM

#### End Date

26-4-2023 12:00 PM

#### Description

We study the problem of maximizing the number of full degree vertices in a spanning tree T of a graph G; that is, the number of vertices whose degree in T equals its degree in G. In cubic graphs, this problem is equivalent to maximizing the number of leaves in T and minimizing the size of a connected dominating set of G. We provide an algorithm that, with high probability, produces a tree with at least 0.437n vertices of full degree when run on a random cubic graph. This improves the previously best known lower bound of 0.4146n.

Full Degree Spanning Trees in Random Cubic Graphs

We study the problem of maximizing the number of full degree vertices in a spanning tree T of a graph G; that is, the number of vertices whose degree in T equals its degree in G. In cubic graphs, this problem is equivalent to maximizing the number of leaves in T and minimizing the size of a connected dominating set of G. We provide an algorithm that, with high probability, produces a tree with at least 0.437n vertices of full degree when run on a random cubic graph. This improves the previously best known lower bound of 0.4146n.