Induced Disjoint Paths in Circular-Arc Graphs in Linear Time

  • Petr A. Golovach
  • Daniël Paulusma
  • Erik Jan van Leeuwen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

Abstract

The Induced Disjoint Paths problem is to test whether a graph \(G\) with \(k\) distinct pairs of vertices \((s_{i},t_{i})\) contains paths \(P_{1},\ldots ,P_{k}\) such that \(P_{i}\) connects \(s_{i}\) and \(t_{i}\) for \(i=1,\ldots ,k\), and \(P_{i}\) and \(P_{j}\) have neither common vertices nor adjacent vertices (except perhaps their ends) for \(1 \le i < j \le k\). We present a linear-time algorithm that solves Induced Disjoint Paths and finds the corresponding paths (if they exist) on circular-arc graphs. For interval graphs, we exhibit a linear-time algorithm for the generalization of Induced Disjoint Paths where the pairs \((s_{i},t_{i})\) are not necessarily distinct.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Daniël Paulusma
    • 2
  • Erik Jan van Leeuwen
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.School of Engineering and Computer ScienceDurham UniversityDurhamUK
  3. 3.Max-Planck Institut für InformatikSaarbrückenGermany

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