Fast partitioning l-apex graphs with applications to approximating maximum induced-subgraph problems

Information Processing Letters

Volumn 61, Issue 5, 1997, Pages 227-232

  Thilikos, Dimitrios M ^a   Bodlaender, Hans L ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Algorithms; Analysis of algorithms; Approximation algorithms; Combinatorial problems; Graph minors; Treewidth

Indexed keywords

EID: 9644284118     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-0190(97)00024-0     Document Type: Article

References (19)

1. N. Alon, P.D. Seymour and R. Thomas, A separator theorem for graphs with an excluded minor and applications, in: Proceedings 22nd Annual Symposium on Theory of Computing (ACM Press, New York, 1990); to appear in J. Amer. Math. Soc.
2. N. Alon, P.D. Seymour and R. Thomas, A separator theorem for graphs with an excluded minor and applications, in: Proceedings 22nd Annual Symposium on Theory of Computing (ACM Press, New York, 1990); to appear in J. Amer. Math. Soc.
3. S. Arnborg and A. Proskurowski, Characterization and recognition of partial 3-trees, SIAM J. Algebraic Discrete Methods 7 (1986) 305-314.
4. B.S. Baker, Approximation algorithms for NP-complete problems on planar graphs, J. ACM 41 (1994) 153-180.
5. D. Bienstock, N. Robertson, P.D. Seymour and R. Thomas, Quickly excluding a forest, J. Combin. Theory Ser. B 52 (1991) 274-283.
6. H.L. Bodlaender, On linear time minor tests with depth first search, J. Algorithms 14 (1993) 1-23.
7. H.L. Bodlaender, On disjoint cycles, Internat. J. Found. Computer Science 5(1) (1994) 59-68.
8. H.L. Bodlaender, A linear time algorithm for finding tree-decompositions of small treewidth, SIAM J. Comput. 25 (1996) 1305-1317.
9. H.L. Bodlaender, R.B. Tan, D.M. Thilikos and J. van Leeuwen, On interval routing schemes and treewidth, in: M. Nagl, ed., Proceedings 21st International Workshop on Graph Theoretic Concepts in Computer Science (WG'95), Lecture Notes in Computer Science 1017 (Springer, Berlin, 1995) 181-186.
10. B. Bollobás, Extremal Graph Theory with Emphasis on Probabilstic Methods, Regional Conference Series in Mathematics (American Mathematical Society, Providence, RI, 1986).
11. N. Chiba, T. Nishizeki and N. Saito, An approximation algorithm for the maximum independent set problem on planar graphs, SIAM J. Comput. 11 (1982) 663-675.
12. M.R. Fellows and M.A. Langston, On search, decision and the efficiency of polynomial-time algorithms, in: Proceedings 21st Annual Symposium on Theory of Computing (ACM Press, New York, 1989) 501-512.
13. R.J. Lipton and R.E. Tarjan, Applications of a planar separator theorem, SIAM J. Comput. 9 (1980) 615-627.
14. W. Mader, Homomorphieeigenshaften und mittlere Kantendichte von Graphen, Math. Ann. 174 (1967) 265-268.
15. N. Robertson and P.D. Seymour, Graph minors. V. Excluding a planar graph, J. Combin. Theory Ser. B 41 (1986) 92-114.
16. N. Robertson, P.D. Seymour and R. Thomas, Quickly excluding a planar graph, J. Combin. Theory Ser. B 62 (1994) 323-348.
17. D.P. Sanders, On linear recognition of tree-width at most four, SIAM J. Algebraic Discrete Methods 19 (1996) 101-119.
18. M. Yannakakis, Node-and edge-deletion NP-complete problems, in: Proceedings 10th Annual Symposium on Theory of Computing (ACM Press, New York, 1978) 253-264.
19. Zhi-Zhong Chen, Practical approximation schemes for maximum induced-subgraph, in: F. Meyer auf der Heide and B. Monien, eds., Proceedings 23rd International Colloquium on Automata, Languages, and Programming (ICALP '96), Lecture Notes in Computer Science 1099 (Springer, Berlin, 1996) 268-279.