, Volume 65, Issue 2, pp 275–316 | Cite as

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)|.


Interval graphs Induced subgraph isomorphism Parameterized complexity 



Supported by the Hungarian National Research Fund OTKA 67651. Schlotter was also supported by the European Union and the European Social Fund (grant TÁMOP 4.2.1./B-09/1/KMR-2010-0003).


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Computer and Automation Research InstituteHungarian Academy of Sciences (MTA SZTAKI)BudapestHungary
  2. 2.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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