Listing All Minimal Separators of a Graph

SIAM Journal on Computing

Volumn 27, Issue 3, 1998, Pages 605-613

  Kloks, T ^a   Kratsch, D ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Algorithm; Good pair; Graph; Listing algorithm; Minimal pair; Minimal separator

Indexed keywords

EID: 0001740507     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S009753979427087X     Document Type: Article

References (20)

1. S. ARNBORG, Efficient algorithms for combinatorial problems on graphs with bounded decomposability - A survey, BIT, 25 (1985), pp. 2-23.
2. S. ARNBORG, J. LAGERGREN, AND D. SEESE, Easy problems for tree-decomposable graphs, J. Algorithms, 12 (1991), pp. 308-340.
3. S. ARNBORG AND A. PROSKUROWSKI, Linear time algorithms for NP-hard problems restricted to partial κ-trees, Discrete Appl. Math., 23 (1989), pp. 305-314.
4. H. BODLAENDER, A tourist guide through treewidth, Acta Cybernet., 11 (1993), pp. 1-21.
5. H. BODLAENDER, A linear time algorithm for finding tree-decompositions of small treewidth, in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 226-234.
6. H. BODLAENDER, T. KLOKS, AND D. KRATSCH, Treewidth and pathwidth of permutation graphs, SIAM J. Discrete Math., 8 (1995), pp. 606-616.
7. H. BODLAENDER, T. KLOKS, D. KRATSCH, AND H. MÜLLER, Treewidth and Minimum Fill-in on d-Trapezoid Graphs, Technical Report UU-CS-1995-34, Utrecht University, The Netherlands, 1995.
8. F. GAVRIL, Algorithms on clique separable graphs, Discrete Math., 19 (1977), pp. 159-165.
9. L. A. GOLDBERG, Efficient Algorithms for Listing Combinatorial Structures, Cambridge University Press, Cambridge, 1993.
10. M. C. GOLUMBIC, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
11. A. KANEVSKY, On the number of minimum size separating vertex sets in a graph and how to find all of them, in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, 1990, pp. 411-421.
12. T. KLOKS, Treewidth - Computations and Approximations, Lecture Notes in Computer Science 842, Springer-Verlag, Berlin, 1994.
13. T. KLOKS, Treewidth of circle graphs, Internat. J. Found. Comput. Sci., 7 (1996), pp. 111-120.
14. T. KLOKS, Minimum Fill-in for Chordal Bipatite Graphs, Technical Report RUU-CS-93-11, Department of Computer Science, Utrecht University, The Netherlands, 1993.
15. T. KLOKS AND D. KRATSCH, Treewidth of chordal bipartite graphs, J. Algorithms 19 (1995), pp. 266-281.
16. T. KLOKS, D. KRATSCH, AND J. SPINRAD, On treewidth and minimum fill-in of asteroidal triple-free graphs, Theoret. Comput. Sci., 175 (1997), pp. 309-335.
17. D. KRATSCH, The Structure of Graphs and the Design of Efficient Algorithms, Habilitation thesis, F.-Schiller-Universität, Jena, Germany, 1996.
18. A. PARRA AND P. SCHEFFLER, How to use the minimal separators of a graph for its chordal triangulation, in Proceedings of the 22rd International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 944, Springer-Verlag, Berlin, 1995, pp. 123-134.
19. R. E. TARJAN, Decomposition by clique separators, Discrete Math., 55 (1985), pp. 221-232.
20. S. H. WHITESIDES, An algorithm for finding clique cut-sets, Inform. Process. Lett., 12 (1981), pp. 31-32.