Grid Minors in Damaged Grids
Keywords: graph theory, grid graphs, graph minors, subgraphs, shallow minors, treewidth, vertex deletion
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.