Year: 2019
Type: preprint
Abstract: Let $L(G)$ denote the maximum number of leaves in any spanning tree of a connected graph $G$. We show the (known) result that for the $n$-cube $Q_n$, $L(Q_n) \sim 2^n = |V(Q_n)|$ as $n\rightarrow \infty$. Examining this more carefully, consider the minimum size of a connected dominating set of vertices $γ_c(Q_n)$, which is $2^n-L(Q_n)$ for $n\ge2$. We show that $γ_c(Q_n)\sim 2^n/n$. We use Hamming codes and an "expansion" method to construct leafy spanning trees in $Q_n$.
Source: arXiv (Cornell University)
Author: Griggs, Jerrold R.
Institution: University of South Carolina
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4288346129