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Finding Maximum Common Biconnected Subgraphs in Series-Parallel Graphs

  • Nils Kriege
  • Petra Mutzel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)

Abstract

The complexity of the maximum common subgraph problem in partial k-trees is still largely unknown. We consider the restricted case, where the input graphs are k-connected partial k-trees and the common subgraph is required to be k-connected. For biconnected outerplanar graphs this problem is solved and the general problem was reported to be tractable by means of tree decomposition techniques. We discuss key obstacles of tree decompositions arising for common subgraph problems that were ignored by previous algorithms and do not occur in outerplanar graphs. We introduce the concept of potential separators, i.e., separators of a subgraph to be searched that not necessarily are separators of the input graph. We characterize these separators and propose a polynomial time solution for series-parallel graphs based on SP-trees.

Keywords

Tree decomposition maximum common subgraph series-parallel graph 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Nils Kriege
    • 1
  • Petra Mutzel
    • 1
  1. 1.Dept. of Computer ScienceTechnische Universität DortmundGermany

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