Independent sets in asteroidal triple-free graphs

  • Hajo Broersma
  • Ton Kloks
  • Dieter Kratsch
  • Haiko Müller
Session 19: Algorithms IV
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)


An asteroidal triple is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called AT-free if it does not have an asteroidal triple. We show that there is an O(n 2 · (¯m+1)) time algorithm to compute the maximum cardinality of an independent set for AT-free graphs, where n is the number of vertices and ¯m is the number of non edges of the input graph. Furthermore we obtain O(n 2 · (¯m+1)) time algorithms to solve the INDEPENDENT DOMINATING SET and the INDEPENDENT PERFECT DOMINATING SET problem on AT-free graphs. We also show how to adapt these algorithms such that they solve the corresponding problem for graphs with bounded asteroidal number in polynomial time. Finally we observe that the problems CLIQUE and PARTITION INTO CLIQUES remain NP-complete when restricted to AT-free graphs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Hajo Broersma
    • 1
  • Ton Kloks
    • 1
  • Dieter Kratsch
    • 2
  • Haiko Müller
    • 2
  1. 1.Faculty of Applied MathematicsUniversity of TwenteAE EnschedeThe Netherlands
  2. 2.Fakultät für Mathematik und InformatikFriedrich-Schiller-UniversitätJenaGermany

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