Characterizing the complexity of subgraph isomorphism for graphs of bounded path-width

  • Arvind Gupta
  • Naomi Nishimura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


We show that the complexity of the subgraph isomorphism problem on graphs of bounded path-width is inherently dependent on the connectivity of the source and target graphs. In particular, for the problem of determining whether a source graph G of path-width k is a subgraph of a target graph H of path-width k, we present an O(n3) algorithm for G and H both k-connected, for n the sum of the sizes of the graphs, and NP-completeness results for connectivity less than k. In previous polynomial-time algorithms, the degree of the polynomial in the running time was a function of k. In contrast, we show that when neither G nor H is k-connected, the problem becomes NP-complete. The same result also holds if one of the graphs has at least k vertices of unbounded degree. Since bounded path-width graphs are also bounded tree-width graphs, our hardness results immediately extend to this larger class. A further NP-completeness result applies to the situation in which both graphs have tree-width k, but only the target graph is k-connected. This provides a complete characterization of the subgraph isomorphism problem on bounded tree-width graphs, thus answering an open question of Matoušek and Thomas.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Arvind Gupta
    • 1
  • Naomi Nishimura
    • 2
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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