Connected domination and steiner set on asteroidal triple-free graphs

  • Hari Balakrishnan
  • Anand Rajaraman
  • C. Pandu Rangan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)


An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighbourhood of the third. Graphs that do not contain an asteroidal triple are called asteroidal triple-free (AT-free) graphs. AT-free graphs strictly contain the well-known class of cocomparability graphs, and are not necessarily perfect. We present efficient polynomial-time algorithms for the minimum cardinality connected dominating set problem and the Steiner set problem on AT-free graphs. These results, in addition to solving these problems on this large class of graphs, also strengthen the conjecture of White. et. al. [9] that these two problems are algorithmically closely related.


Design of algorithms asteroidal-triple free graphs 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. Arvind and C. Pandu Rangan. Connected domination and Steiner set on weighted permutation graphs. Info. Proc. Letts., 41:215–220, 1992.CrossRefGoogle Scholar
  2. [2]
    C.J. Colburn and L.K. Stewart. Permutation graphs: Connected domination and Steiner trees. Discrete Math., 86:145–164, 1990.CrossRefGoogle Scholar
  3. [3]
    D.G. Corneil, S. Olariu, and L. Stewart. Asteroidal triple-free graphs. Technical Report 262/92, University of Toronto, June 1992.Google Scholar
  4. [4]
    D.G. Corneil and L.K. Stewart. Dominating sets in perfect graphs. Discrete Math., 86:179–189, 1990.CrossRefGoogle Scholar
  5. [5]
    A. D'Atri and M. Mascarini. Distance hereditary graphs, Steiner trees and connected domination. SIAM J. Computing, 17:521–538, 1988.CrossRefGoogle Scholar
  6. [6]
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Fransisco, CA, 1979.Google Scholar
  7. [7]
    M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, 1980.Google Scholar
  8. [8]
    C.G. Lekkerkerker and J.C. Boland. Representation of a finite graph by a set of intervals on a real line. Fundamenta Mathematicae, 51:45–64, 1962.Google Scholar
  9. [9]
    K. White, M. Farber, and W.R. Pulleybank. Steiner trees, connected domination and strongly chordal graphs. Networks, 15:109–124, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Hari Balakrishnan
    • 1
  • Anand Rajaraman
    • 1
  • C. Pandu Rangan
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyMadrasIndia

Personalised recommendations