A generalization of the pentomino exclusion problem: Dislocation of graphs Original Research Article

In this paper, we first investigate the pentomino exclusion problem, due to Golomb. We solve this problem on the image grid and we give some lower and upper bounds for the image grid for all image and image. We then give a generalization of this problem in graphs, the image-dislocation problem, which consists in finding the minimum number of vertices to be removed from a graph so as all the remaining connected components have cardinality at most image. We investigate the algorithmic aspects of the image-dislocation problem: we first prove the problem is NP-Complete, then we give a sublinear algorithm which solves the problem on a restricted class of graphs which includes the image grid graphs, provided image is not part of the input.