Parameterized Graph Cleaning Problems

Dániel Marx, Ildikó Schlotter

Abstract: We investigate the Induced Subgraph Isomorphism problem with non-standard parametrization, 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.