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arXiv · 2105.05797

Regular grid subgraphs of maximal girth

Jan Kristian Haugland
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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.

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Jan Kristian Haugland. 2021-05-11. Regular grid subgraphs of maximal girth. https://arxiv.org/abs/2105.05797

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