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.