Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903645 | European Journal of Combinatorics | 2018 | 17 Pages |
Abstract
The complexity of the maximum common connected subgraph problem in partial k-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial 2-trees. On the other hand, the problem is known to be NP-hard in vertex-labeled partial 11-trees of bounded degree. We consider series-parallel graphs, i.e., partial 2-trees. We show that the problem remains NP-hard in biconnected series-parallel graphs with all but one vertex of degree 3 or less. A positive complexity result is presented for a related problem of high practical relevance which asks for a maximum common connected subgraph that preserves blocks and bridges of the input graphs. We present a polynomial time algorithm for this problem in series-parallel graphs, which utilizes a combination of BC- and SP-tree data structures to decompose both graphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Nils Kriege, Florian Kurpicz, Petra Mutzel,