Linear time algorithms for dominating pairs in asteroidal triple-free graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 944, Issue , 1995, Pages 292-302

  Corneil, Derek G ^a   Olariu, Stephan ^b   Stewart, Lorna ^c  

^a UNIVERSITY OF TORONTO   (Canada)

^b OLD DOMINION UNIVERSITY   (United States)

^c UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; AUTOMATA THEORY; CLUSTERING ALGORITHMS; COMPUTATIONAL LINGUISTICS; GRAPHIC METHODS;

ASTEROIDAL TRIPLE-FREE; ASTEROIDAL TRIPLES; COCOMPARABILITY GRAPHS; CONSTRUCTIVE PROOF; INDEPENDENT SET; LEXICOGRAPHIC BREADTH FIRST SEARCH; LINEAR-TIME ALGORITHMS; SIMPLE ALGORITHM;

GRAPH THEORY;

EID: 84958037675     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-60084-1_82     Document Type: Conference Paper

References (18)

1. K. A. Baker, P. C. Fishburn, and F. S. Roberts, Partial orders of dimension two, Networks, 2 (1971), 11-28.
2. H. Balakrishnan, A. Rajaraman and C. Pandu Rangan, Connected domination and Steiner set on asteroidal triple-free graphs, Proc. Workshop on Algorithms and Data Structures, WADS'93, Montreal, Canada, August 1993, LNCS, Vol. 709, F. Dehne, J.-R. Sack, N. Santoro, S. Whitesides (Eds.), Springer-Verlag, Berlin, 1993, 131-141.
3. J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, North-Holland, Amsterdam, 1976.
4. K. S. Booth and G. S. Lueker, Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms, Journal of Comput. Syst. Sci., 13 (1976), 335-379.
5. K. S. Booth and G. S. Lueker, A linear time algorithm for deciding interval graph isomorphism, Journal of the ACM, 26 (1979), 183-195.
6. D.G. Corneil and P.A. Kamula, Extensions of permutation and interval graphs, Proceedings 18th Southeastern Conference on Combinatorics, Graph Theory and Computing, 1987, 267-276.
7. D.G. Corneil, S. Olariu and L. Stewart, Asteroidal triple-free graphs, Proc. 19th International Workshop on Graph Theoretic Concepts in Computer Science, WG'93, Utrecht, The Netherlands, June 1993, LNCS, Vol. 790, J. van Leeuwen (Ed.), Springer-Verlag, Berlin, 1994, 211-224.
8. D.G. Corneil, S. Olariu and L. Stewart, A linear time algorithm to compute a dominating path in an AT-free graph, Information Processing Letters, to appear.
9. D.G. Corneil, S. Olariu and L. Stewart, Asteroidal triple-free graphs, Technical Report TR-94-31, Department of Computer Science, Old Dominion University, November 1994, submitted for publication.
10. D.G. Corneil, S. Olariu and L. Stewart, Linear time algorithms for dominating pairs in asteroidal triple-free graphs, Technical Report 294/95, Department of Computer Science, University of Toronto, January 1995, submitted for publication.
11. I. Dagan, M.C. Golumbic and R.Y. Pinter, Trapezoid graphs and their coloring, Discrete Applied Mathematics, 21 (1988), 35-46.
12. S. Even, A. Pnueli and A. Lempel, Permutation graphs and transitive graphs, Journal of the ACM, 19 (1972), 400-410.
13. M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
14. M.C. Golumbic, C.L. Monma and W.T. Trotter Jr.., Tolerance graphs, Discrete Applied Mathematics, 9 (1984), 157-170.
15. D. Kratsch and L. Stewart, Domination on cocomparability graphs, SIAM Journal on Discrete Mathematics, 6 (1993), 400-417.
16. C.G. Lekkerkerker and J.C. Boland, Representation of a finite graph by a set of intervals on the real line, Fundamenta Mathematicae, 51 (1962), 45-64.
17. D.J. Rose, R.E. Tarjan, G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM Journal on Computing, 5 (1976), 266-283.
18. R.E. Tarjan and M. Yannakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs, SIAM Journal on Computing, 13 (1984), 566-579.