International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 200-212 | Cite as

On Maximum Common Subgraph Problems in Series-Parallel Graphs

  • Nils Kriege
  • Florian KurpiczEmail author
  • Petra Mutzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)


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 contrary, 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 bounded by three. 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.


Maximum Common Subgraph Block and Bridge Preserving Series-parallel graphs 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceTechnische Universität DortmundDortmundGermany

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