Computing a dominating pair in an asteroidal triple-free graph in linear time

  • Derek G. Corneil
  • Stephan Olariu
  • Lorna Stewart
Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 955)


An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triple-free (AT-free, for short) if it contains no asteroidal triple. The motivation for this work is provided, in part, by the fact that AT-free graphs offer a common generalization of interval, permutation, trapezoid, and cocomparability graphs. Previously, the authors have given an existential proof of the fact that every connected AT-free graph contains a dominating pair, that is, a pair of vertices such that every path joining them is a dominating set in the graph. The main contribution of this paper is a constructive proof of the existence of dominating pairs in connected AT-free graphs. The resulting simple algorithm can be implemented to run in time linear in the size of the input, whereas the best algorithm previously known for this problem has complexity OV¦3) for input graph G=(V, E).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Derek G. Corneil
    • 1
  • Stephan Olariu
    • 2
  • Lorna Stewart
    • 3
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.Department of Computer ScienceOld Dominion UniversityNorfolkUSA
  3. 3.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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