2021/05/11 by Haugland, Jan Kristian
#00-02 (Primary) 05C62 (Secondary) #FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2105.05797
The unit-distance graph on the n-dimensional integer lattice ℤn 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.