Listing all potential maximal cliques of a graph

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

Volumn 1770, Issue , 2000, Pages 503-515

  Bouchitté, Vincent ^a   Todinca, Ioan ^a  

^a UNIV LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

SEPARATORS;

MAXIMAL CLIQUE; MINIMAL TRIANGULATIONS; POLYNOMIAL NUMBER; POLYNOMIAL-TIME; TREE-WIDTH; VERTEX SET;

POLYNOMIAL APPROXIMATION;

EID: 84944078742     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46541-3_42     Document Type: Conference Paper

References (30)

1. S. Arnborg, D.G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM J. on Algebraic and Discrete Methods, 8:277-284, 1987.
2. S. Arnborg, B. Courcelle, A. Proskurowski, and D. Seese. An algebraic theory of graph reduction. J. of ACM, 40:1134-1164, 1993.
3. S. Arnborg and A. Proskurowski. Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Applied Mathematics, 23:11-24, 1989.
4. A. Berry, J.P. Bordat, and O. Cogis. Generating all the minimal separators of a graph. In Workshop on Graphs WG'99, Lecture Notes in Computer Science. Springer-Verlag, 1999.
5. H. Bodlaender. A tourist guide through treewidth. Acta Cybernetica, 11:1-23, 1993.
6. H. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. Siam J. Computing, 25:1305-1317, 1996.
7. H. Bodlaender. Treewidth: Algorithmic techniques and results. In Proceedings of MFCS'97, volume 1295 of Lecture Notes in Computer Science, pages 19-36. Springer-Verlag, 1997.
8. H. Bodlaender and B. de Fluiter. Reduction algorithms for constructing solutions of graphs with small treewidth. In Proceedings of COCOON'96, volume 1090 of Lecture Notes in Computer Science, pages 199-208. Springer-Verlag, 1996.
9. H. Bodlaender, J.R. Gilbert, H. Hafsteinsson, and T. Kloks. Approximating treewidth, pathwidth, and minimum elimination tree height. J. of Algorithms, 18:238-255, 1995.
10. V. Bouchitt_e and I. Todinca. Minimal triangulations for graphs with “few" minimal separators. In Proceedings 6th Annual European Symposium on Algorithms (ESA'98), volume 1461 of Lecture Notes in Computer Science, pages 344-355. Springer-Verlag, 1998.
11. V. Bouchitté and I. Todinca. Treewidth and minimum fill-in of weakly triangulated graphs. In Proceedings 16th Symposium of Theoretical Aspects in Computer Science (STACS'99), volume 1563 of Lecture Notes in Computer Science, pages 197-206. Springer-Verlag, 1999.
12. M. S. Chang. Algorithms for maximum matching and minimum fill-in on chordal bipartite graphs. In ISAAC'96, volume 1178 of Lecture Notes in Computer Sci- ence, pages 146-155. Springer-Verlag, 1996.
13. B. Courcelle. The monadic second-order logic of graphs III: Treewidth, forbidden minors and complexity issues. Informatique Théorique, 26:257-286, 1992.
14. B. Courcelle and M. Moshbah. Monadic second-order evaluations on treedecomposable graphs. Theoretical Computer Science, 109:49-82, 1993.
15. M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
16. T. Hagerup. Dynamic algorithms for graphs of bounded treewidth. In Proceed- ings 24th International Colloquium on Automata, Languages, and Programming (ICALP'97), Lecture Notes in Computer Science, pages 292-302. Springer-Verlag, 1997.
17. T. Kloks, H.L. Bodlaender, H. Müller, and D. Kratsch. Computing treewidth and minimum _ll-in: all you need are the minimal separators. In Proceedings First Annual European Symposium on Algorithms (ESA'93), volume 726 of Lecture Notes in Computer Science, pages 260-271. Springer-Verlag, 1993.
18. T. Kloks, H.L. Bodlaender, H. Müller, and D. Kratsch. Erratum to the ESA'93 proceedings. In Proceedings Second Annual European Symposium on Algorithms (ESA'94), volume 855 of Lecture Notes in Computer Science, page 508. Springer- Verlag, 1994.
19. T. Kloks and D. Kratsch. Treewidth of chordal bipartite graphs. J. Algorithms, 19(2):266-281, 1995.
20. T. Kloks and D. Kratsch. Listing all minimal separators of a graph. SIAM J. Comput., 27(3):605-613, 1998.
21. T. Kloks, D. Kratsch, and H. Müller. Approximating the bandwidth for asteroidal triple-free graphs. In Proceedings Third Annual European Symposium on Algorithms (ESA'95), volume 979 of Lecture Notes in Computer Science, pages 434-447. Springer-Verlag, 1995.
22. T. Kloks, D. Kratsch, and J. Spinrad. On treewidth and minimum fill-in of asteroidal triple-free graphs. Theoretical Computer Science, 175:309-335, 1997.
23. T. Kloks, D. Kratsch, and C.K. Wong. Minimum fill-in of circle and circular-arc graphs. J. Algorithms, 28(2):272-289, 1998.
24. A. Parra and P. Scheffer. Characterizations and algorithmic applications of chordal graph embeddings. Discrete Appl. Math., 79(1-3):171-188, 1997.
25. N. Robertson and P. Seymour. Graphs minors. III. Planar tree-width. J. of Combinatorial Theory Series B, 36:49-64, 1984.
26. N. Robertson and P. Seymour. Graphs minors. II. Algorithmic aspects of treewidth. J. of Algorithms, 7:309-322, 1986.
27. D.J. Rose. Triangulating graphs and the elimination process. J. Math Anal Appl., 32:597-609, 1970.
28. R. Sundaram, K. Sher Singh, and C. Pandu Rangan. Treewidth of circular-arc graphs. SIAM J. Discrete Math., 7:647-655, 1994.
29. I. Todinca. Aspects algorithmiques des triangulations minimales des graphes. PhD thesis, École Normale Supérieure de Lyon, 1999.
30. M. Yannakakis. Computing the minimum fill-in is NP-complete. SIAM Journal on Algebraic and Discrete Methods, 2:77-79, 1981.