Vertex disjoint paths on clique-width bounded graphs

Theoretical Computer Science

Volumn 359, Issue 1-3, 2006, Pages 188-199

  Gurski, Frank ^a   Wanke, Egon ^a  

^a HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

Clique width; Edge disjoint paths; Line graphs; NLC width; Tree width; Vertex disjoint paths

Indexed keywords

COMPUTER SCIENCE; POLYNOMIALS; PROBLEM SOLVING; TREES (MATHEMATICS);

CLIQUE-WIDTH; EDGE DISJOINT PATHS; LINE GRAPHS; NLC-WIDTH; TREE-WIDTH; VERTEX DISJOINT PATHS;

GRAPH THEORY;

EID: 33746356242     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2006.02.026     Document Type: Article

References (29)

1. S. Alstrup, C. Gavoille, H. Kaplan, T. Rauhe, Nearest common ancestors: A survey and a new distributed algorithm. in: Proc. Annu. ACM Symp. Parallel Algorithms and Architectures, ACM, 2002, pp. 258-264.
2. Bodlaender H.L. Polynomial algorithms for chromatic index and graph isomorphism on partial k-trees. J. Algorithms 11 4 (1990) 631-643
3. A. Brandstädt, F.F. Dragan, H.-O. Le, R. Mosca, New graph classes of bounded clique width, in: Proc. Graph-Theoretical Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 2573, Springer, Berlin, 2002, pp. 57-67.
4. D.G. Corneil, M. Habib, J.M. Lanlignel, B. Reed, U. Rotics, Polynomial time recognition of clique-width at most three graphs, in: Proc. Latin American Symp. on Theoretical Informatics, Lecture Notes in Computer Science, Vol. 1776, Springer, Berlin, 2000, pp. 126-134.
5. Corneil D.G., Perl Y., and Stewart L.K. A linear recognition algorithm for cographs. SIAM J. Comput. 14 4 (1985) 926-934
6. D.G. Corneil, U. Rotics, On the relationship between clique-width and treewidth, in: Proc. Graph-Theoretical Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 2204, Springer, Berlin, 2001, pp. 78-90.
7. Courcelle B., Makowsky J.A., and Rotics U. Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Systems 33 2 (2000) 125-150
8. Courcelle B., and Olariu S. Upper bounds to the clique width of graphs. Discrete Appl. Math. 101 (2000) 77-114
9. W. Espelage, F. Gurski, E. Wanke, How to solve NP-hard graph problems on clique-width bounded graphs in polynomial time, in: Proc. Graph-Theoretical Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 2204, Springer, Berlin, 2001, pp. 117-128.
10. Espelage W., Gurski F., and Wanke E. Deciding clique-width for graphs of bounded tree-width. J. Graph Algorithms Appl.-Special Issue JGAA WADS 2001 7 2 (2003) 141-180
11. Even S., Itai A., and Shamir A. On the complexity of timetable and multicommodity flow problems. SIAM J. Comput. 5 (1976) 691-703
12. T. Feder, R. Motwani, Clique partitions, graph compression and speeding up algorithms, in: Proc. Annu. ACM Symp. on Theory of Computing, ACM, 1991, pp. 123-133.
13. M.R. Fellows, F.A. Rosamund, U. Rotics, S. Szeider, Proving NP-hardness for clique-width I: non-approximability of sequential clique-width, Technical Report TR05-080, ECCC, 2005.
14. M.R. Fellows, F.A. Rosamund, U. Rotics, S. Szeider, Proving NP-hardness for clique-width II: non-approximability of clique-width, Technical Report TR05-081, ECCC, 2005.
15. Golumbic M.C., and Rotics U. On the clique-width of some perfect graph classes. Internat. J. Found. Comput. Sci. 11 3 (2000) 423-443
16. n, n, in: Proc. Graph-Theoret. Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 1938, Springer, Berlin, 2000, pp. 196-205.
17. F. Gurski, E. Wanke, Minimizing NLC-width is NP-complete (Extended Abstract), in: Proc. Graph-Theoretical Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 3787, Springer, Berlin, 2005, pp. 69-80.
18. Johansson O. Clique-decomposition, NLC-decomposition, and modular decomposition-relationships and results for random graphs. Congr. Numer. 132 (1998) 39-60
19. 2-decomposition in polynomial time. Internat. J. Found. Comput. Sci. 11 3 (2000) 373-395
20. Kobler D., and Rotics U. Edge dominating set and colorings on graphs with fixed clique-width. Discrete Appl. Math. 126 2-3 (2003) 197-221
21. Middendorf M., and Pfeiffer F. On the complexity of the disjoint paths problems. Combinatorica 35 1 (1995) 97-107
22. Nishizeki T., Vygen J., and Zhou X. The edge-disjoint paths problem is NP-complete for series-parallel graphs. Discrete Appl. Math. 115 (2001) 177-186
23. S.-I. Oum, P.D. Seymour, Approximating clique-width and branch-width, J. Combin. Theory, Ser. B, 2006, to appear.
24. Robertson N., and Seymour P.D. Graph minors II. Algorithmic aspects of tree width. J. Algorithms 7 (1986) 309-322
25. Robertson N., and Seymour P.D. Graph minors XII. The disjoint paths problem. J. Combin. Theory, Ser. B 63 1 (1995) 65-110
26. Rose D.J. On simple characterizations of k-trees. Discrete Math. 7 (1974) 317-322
27. P. Scheffler, A practical linear time algorithm for vertex disjoint paths in graphs with bounded treewidth, Technical Report 396, Department of Mathematics, Technische Universität Berlin, 1994.
28. I. Todinca, Coloring powers of graphs of bounded clique-width, in: Proc. Graph-Theoret. Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 2880, Springer, Berlin, 2003, pp. 370-382.
29. Wanke E. k-NLC graphs and polynomial algorithms. Discrete Appl. Math. 54 (1994) 251-266