TY - JOUR
T1 - Full degree spanning trees in random regular graphs
AU - Acquaviva, Sarah
AU - Bal, Deepak
N1 - Publisher Copyright:
© 2024 Elsevier B.V.
PY - 2024/8/15
Y1 - 2024/8/15
N2 - 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.
AB - 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.
KW - Algorithms
KW - Differential equations method
KW - Random regular graphs
KW - Spanning trees
UR - http://www.scopus.com/inward/record.url?scp=85191302485&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2024.04.010
DO - 10.1016/j.dam.2024.04.010
M3 - Article
AN - SCOPUS:85191302485
SN - 0166-218X
VL - 353
SP - 85
EP - 93
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -