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.Comment: 12 pages, 5 figures. This version adds an application to treewidth
  criticality, strengthens the upper and lower bounds for hypercube subgraphs,
  and includes a new discussion of connections to coding theor