Year: 2021
Type: preprint
Abstract: The unit-distance graph on the $n$-dimensional integer lattice $\mathbb{Z}^n$ is called the $n$-dimensional grid. We attempt to maximize the girth of a $k$-regular (possibly induced) subgraph of the $n$-dimensional grid, and provide examples and bounds for selected values of $n$ and $k$, along with more general results. A few cases involving alternative lattices are also considered.
Source: arXiv (Cornell University)
Author: Haugland, Jan Kristian
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3163889360