Chordless Paths Through Three Vertices

  • Robert Haas
  • Michael Hoffmann
Conference paper

DOI: 10.1007/978-3-540-28639-4_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3162)
Cite this paper as:
Haas R., Hoffmann M. (2004) Chordless Paths Through Three Vertices. In: Downey R., Fellows M., Dehne F. (eds) Parameterized and Exact Computation. IWPEC 2004. Lecture Notes in Computer Science, vol 3162. Springer, Berlin, Heidelberg

Abstract

Consider the following problem, that we call “Chordless Path through Three Vertices” or Cp3v, for short: Given a simple undirected graph G=(V,E), a positive integer k, and three distinct vertices s, t, and vV, is there a chordless path from s via v to t in G that consists of at most k vertices? In a chordless path, no two vertices are connected by an edge that is not in the path. Alternatively, one could say that the subgraph induced by the vertex set of the path in G is the path itself. The problem has been raised in the context of service deployment in communication networks. We resolve the parametric complexity of Cp3v by proving it W[1]-complete with respect to its natural parameter k. Our reduction extends to a number of related problems about chordless paths. In particular, deciding on the existence of a single directed chordless (s,t)-path in a digraph is also W[1]-complete with respect to the length of the path.

Keywords

graph theory induced path parameterized complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Robert Haas
    • 1
  • Michael Hoffmann
    • 2
  1. 1.IBM Zurich Research LaboratoryRüschlikon
  2. 2.Institute for Theoretical Computer ScienceETH Zürich 

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