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 -