On treewidth and minimum fill-in of asteroidal triple-free graphs

Theoretical Computer Science

Volumn 175, Issue 2, 1997, Pages 309-335

  Kloks, Ton ^a   Kratsch, Dieter ^b   Spinrad, Jeremy ^c  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; GRAPH THEORY; POLYNOMIALS;

ASTEROIDAL TRIPLE FREE GRAPHS; PATHWIDTH; TIME ALGORITHMS; TREEWIDTH;

ALGORITHMS;

EID: 0031118743     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(96)00206-X     Document Type: Article

References (24)

1. S. Arnborg, D.G. Cornell and A. Proskurowski, Complexity of finding embeddings in a k-tree, SIAM J. Algeb. Discrete Methods 8 (1987) 277-284.
2. H. Bodlaender, A tourist guide through treewidth, Acta Cybernet. 11 (1993) 1-23.
3. H. Bodlaender, T. Kloks and D. Kratsch, Treewidth and pathwidth of permutation graphs, SIAM J. Discrete Math. 8 (1995) 606-616.
4. H. Bodlaender, T. Kloks, D. Kratsch and H. Müller, Treewidth and minimum fill-in on d-trapezoid graphs, manuscript, 1996.
5. D.G. Corneil, S. Olariu and L. Stewart, Asteroidal triple-free graphs, in: Proc. 19th Internal. Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science. Vol. 790 (Springer, Berlin, 1994) 211-224.
6. D.G. Corneil, S. Olariu and L. Stewart, A linear time algorithm to compute dominating pairs in asteroidal triple-free graphs, in: Proc. 22nd Internat. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 944 (Springer, Berlin, 1995) 292-302.
7. G.A. Dirac, On rigid circuit graphs, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 25 (1961) 71-76.
8. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).
9. M. Habib and R.H. Möhring, Treewidth of cocomparability graphs and a new order-theoretic parameter, Order 11 (1994) 47-60.
10. T. Kloks, Treewidth - Computations and Approximations, Lecture Notes in Computer Science, Vol. 842 (Springer, Berlin, 1994).
11. T. Kloks and D. Kratsch, Finding all minimal separators of a graph, in: Proc. 11th Ann. Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 775 (Springer, Berlin, 1994) 759-768; also to appear in SIAM J. Comput.
12. T. Kloks and D. Kratsch, Finding all minimal separators of a graph, in: Proc. 11th Ann. Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 775 (Springer, Berlin, 1994) 759-768; also to appear in SIAM J. Comput.
13. T. Kloks, D. Kratsch and H. Müller, Approximating the bandwidth of AT-free graphs, in: Proc. 3rd European Symp. on Algorithms, Lecture Notes in Computer Science, Vol. 979 (Springer, Berlin, 1995), 434-447.
14. D. Kratsch, The structure of graphs and the design of efficient algorithms, Habilitation, Thesis, Friedrich-Schiller-Universität Jena, 1996.
15. J. van Leeuwen, Graph algorithms, in: Handbook of Theoretical Computer Science, A: Algorithms and Complexity Theory (North-Holland, Amsterdam, 1990) 527-631.
16. R.H. Möhring, Triangulating graphs without asteroidal triples, Discrete Appl. Math. 64 (1996) 281-287.
17. T. Ohtsuki, A fast algorithm for finding an optimal ordering for vertex elimination on a graph, SIAM J. Comput. 5 (1976) 133-145.
18. A. Parra and P. Scheffler, How to use the minimal separators of a graph for its chordal triangulation, in: Proc. 22nd Internal. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 944 (Springer, Berlin, 1995) 123-134.
19. D.J. Rose, Triangulated graphs and the elimination process, J. Math. Anal. Appl. 32 (1970) 597-609.
20. D.J. Rose, R.E. Tarjan and G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput. 5 (1976) 266-283.
21. J. Spinrad, On comparability and permutation graphs, SIAM J. Comput. 14 (1985) 658-670.
22. W.T. Trotter, Combinatorics and Partially Ordered Sets: Dimension Theory (John Hopkins University Press, Baltimore, MD, 1992).
23. M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 2 (1981) 77-79.
24. M. Yannakakis, The complexity of the partial order dimension problem, SIAM J. Algebraic Discrete Methods 3 (1982) 351-358.