Parameterized graph cleaning problems Original Research Article

We investigate the Induced Subgraph Isomorphism problem with non-standard parameterization, where the parameter is the difference image with image and image being the smaller and the larger input graph, respectively. Intuitively, we can interpret this problem as “cleaning” the graph image, regarded as a pattern containing extra vertices indicating errors, in order to obtain the graph image representing the original pattern. We show fixed-parameter tractability of the cases where both image and image are planar and image is 3-connected, or image is a tree and image is arbitrary. We also prove that the problem when image and image are both 3-connected planar graphs is NP-complete without parameterization.