TL;DR
This paper establishes tight bounds on the size of grid minors and subgraphs in damaged grid graphs, extending results to higher dimensions with less precision.
Contribution
It provides tight bounds on grid minors in damaged grids and extends the analysis to higher-dimensional grids with less tight bounds.
Findings
Bounds are tight within constant factors for 2D damaged grids.
Extended bounds for higher-dimensional damaged grids.
Results improve understanding of grid minors in imperfect grid structures.
Abstract
We prove upper and lower bounds on the size of the largest square grid graph that is a subgraph, minor, or shallow minor of a graph in the form of a larger square grid from which a specified number of vertices have been deleted. Our bounds are tight to within constant factors. We also provide less-tight bounds on analogous problems for higher-dimensional grids.
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