Maximum Common Subgraph: Upper Bound and Lower Bound Results

Huang, Xiuzhen; Lai, Jing

doi:10.1109/imsccs.2006.84

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2009

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“…Such operations could involve the deletion of edges, or contraction of vertices or edges. By allowing the deletion of a certain number of vertices to be applied on the smaller graph also we obtain the Maximum Common Induced Subgraph problem [19]. To our knowledge, none of these natural questions have been studied using the non-standard parametrization examined in this paper.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Parameterized graph cleaning problems

Marx

Schlotter

2009

Discrete Applied Mathematics

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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. We also prove that the problem when H and G are both 3-connected planar graphs is NP-complete without parametrization.

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Section: Conclusion and Open Problemsmentioning

confidence: 99%