Document Type
Preprint
Publication Date
8-15-2024
Journal / Book Title
Discrete Applied Mathematics
Abstract
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 produces (w.h.p.) a tree with at least 0.4591n vertices of full degree (and also, leaves) when run on a random cubic graph. This improves the previously best known lower bound of 0.4146n. We also provide lower bounds on the number of full degree vertices in the random regular graph G(n,r) for r≤10.
DOI
10.1016/j.dam.2024.04.010
MSU Digital Commons Citation
Acquaviva, Sarah and Bal, Deepak, "Full degree spanning trees in random regular graphs" (2024). Department of Mathematics Faculty Scholarship and Creative Works. 226.
https://digitalcommons.montclair.edu/mathsci-facpubs/226