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Cleaning Interval Graphs

We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard parameterization, where the parameter is the difference |V(G)|-|V(H)|, with G and H being the larger and the smaller 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 also prove W[1]-hardness for the standard parameterization where the parameter is |V(H)|.