Montclair State University Digital Commons - Student Research Symposium: Full Degree Spanning Trees in Random Cubic Graphs
 

Full Degree Spanning Trees in Random Cubic Graphs

Presenter Information

Sarah Acquaviva
Deepak Bal

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.

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Apr 26th, 11:00 AM Apr 26th, 12:00 PM

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.