Minimum dominating cycles in 2-trees
- 47 Downloads
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 wordsGraph theory algorithm 2-tree domination Hamiltonian cycle
Unable to display preview. Download preview PDF.
- 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.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.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.E. J. Cockayne and S. T. Hedetniemi, “Towards a theory of domination in graphs,”Networks 7:247–261 (1977).Google Scholar
- 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.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.A. Proskurowski, “Minimum Dominating Cycles of Maximal Outerplanar Graphs,” CS-TR-77-4, University of Oregon.Google Scholar
- 8.A. Proskurowski, “Shortest Paths in Recursive Graphs,” CS-TR-78-10, University of Oregon.Google Scholar
- 9.P. Slater, “R-domination in graphs,”JACM 23:446–450 (1976).Google Scholar