Grid Minors in Damaged Grids

David Eppstein

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.


Keywords


graph theory; grid graphs; graph minors; subgraphs; shallow minors; treewidth; vertex deletion

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