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