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Minimum dominating cycles in 2-trees

  • Andrzej Proskurowski
Article

Abstract

We consider the class of 2-trees and present a linear time algorithm for finding minimum dominating cycles of such graphs. We stress the use of a particular representation of these graphs called a recursive representation, and some linear operations on directed trees associated with these graphs.

Key words

Graph theory algorithm 2-tree domination Hamiltonian cycle 

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References

  1. 1.
    D. W. Bange, A. E. Barkauskas, and P. Slater, “Using associated trees to count the spanning trees of labeled maximal outerplanar graphs,“Proceedings of the Eighth S-E Conference on Combinatorics, Graph Theory, and Computing, pp. 605–614.Google Scholar
  2. 2.
    T. Beyer, W. Jones, and S. Mitchell, “Linear Algorithm for Isomorphism of Maximal Outer Planar Graphs,” CS-TR-78-1, University of Oregon, to appear inJACM.Google Scholar
  3. 3.
    E. J. Cockayne, S. E. Goodman, and S. T. Hedetniemi, “A linear algorithm for the domination number of a tree,”Inf. Process. Lett. 4:41–44 (1975).Google Scholar
  4. 4.
    E. J. Cockayne and S. T. Hedetniemi, “Towards a theory of domination in graphs,”Networks 7:247–261 (1977).Google Scholar
  5. 5.
    L. Lesniak-Foster and J. E. Williamson, “On spanning and dominating circuits in graphs,”Can. Math. Bull. 20(2):215–220 (June 1977).Google Scholar
  6. 6.
    S. Mitchell, “Algorithms on Trees and Maximal Outer Planar Graphs: Design, Complexity Analysis, and Data Structures Studies,” PhD thesis, University of Virginia (1976).Google Scholar
  7. 7.
    A. Proskurowski, “Minimum Dominating Cycles of Maximal Outerplanar Graphs,” CS-TR-77-4, University of Oregon.Google Scholar
  8. 8.
    A. Proskurowski, “Shortest Paths in Recursive Graphs,” CS-TR-78-10, University of Oregon.Google Scholar
  9. 9.
    P. Slater, “R-domination in graphs,”JACM 23:446–450 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • Andrzej Proskurowski
    • 1
  1. 1.Department of Computer ScienceUniversity of OregonEugene

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