Parameterized graph cleaning problems

Authors:
Dániel Marx;Ildikó Schlotter
Affiliations:
Department of Computer Science and Information Theory, Budapest University of Technology and Economics, H-1521 Budapest, Hungary;Department of Computer Science and Information Theory, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
Venue:
Discrete Applied Mathematics
Year:
2009

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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.