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.
Research supported by the German Research Foundation (DFG), priority programme “Algorithms for Big Data” (SPP 1736).
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Kriege, N., Mutzel, P. (2014). Finding Maximum Common Biconnected Subgraphs in Series-Parallel Graphs. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_43
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DOI: https://doi.org/10.1007/978-3-662-44465-8_43
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