On parameterized path and chordless path problems

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2007, Pages 250-263

  Chen, Yijia ^a   Flum, Jörg ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; PARAMETERIZATION; PROBLEM SOLVING; THEOREM PROVING;

CHORDLESS PATH PROBLEMS; MAXIMAL LENGTH PATH; PARAMETERIZED PATHS;

GRAPH THEORY;

EID: 34748908418     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2007.21     Document Type: Conference Paper

References (27)

1. N. Alon, R. Yuster, and U. Zwick. Color-coding. Journal of the ACM, 42:844-856, 1995.
2. N. Alon, R. Yuster, and U. Zwick. Finding and counting given length cycles. Algorithmica, 17:209-223, 1997.
3. P. Cameron. Combinatorics. Cambridge University Press, 1994.
4. Y. Chen and J. Flum. The parameterized complexity of maximality and minimality problems. In Proceedings of the 2nd International Workshop on Parameterized and Exact Computation, volume 4169 of Lecture Notes in Computer Science, 25-37, Springer-Verlag, 2006.
5. M. Chudnovsky, G. Cornuéjols, X. Liu, P. D. Seymour, and K. Vuskovic. Recognizing Berge graphs. Combinatorica, 25:143-186,2005.
6. M. Chudnovsky, K Kawarabayashi, and P. Seymour. Detecting even holes. Journal of Graph Theory, 48:85-111, 2005.
7. M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas. The strong perfect graph theorem. Annals of Mathematics, 164:51-229, 2006.
8. M. Conforti, G. Cornuéjols, A.Kapoor, K., and Vuskovic. Even-hole free graphs Part II: recognition algorithm. Journal of Graph Theory, 40: 238-266, 2002
9. G. Cornuéjols. The strong perfect graph theorem. Optima, 70:2-6, 2003.
10. R.G. Downey and M.R. Fellows. Fixed-parameter tractability and completeness. Congressus Numerantium, 87:161-178, 1992.
11. R.G. Downey and M.R. Fellows. Parameterized Complexity. Springer-Verlag, 1999.
12. J. Flum and M. Grohe. The parameterized complexity of counting problems. SIAM Journal on Computing, 33:892-922 2005.
13. J. Flum and M. Grohe. Parameterized Complexity Theory. Springer-Verlag, 2006.
14. 2n nondeterministic bits. Journal of Computer and System Sciences, 72:34-71, 2006.
15. M. Grohe. The complexity of generalized model-checking problems. Unpublished manuscript.
16. R. Haas and M. Hoffmann. Chordless paths through three vertices. Theoretical Computer Science, 351:360-371, 2006.
17. S. Hedetniemi. Problem 23, Algorithms and complexity problems, Open problems in combinatorial optimization. Available at http://www.cs.clemson.edu/ ~hedet/algorithms.html.
18. R. Impagliazzo, R.Paturi, and F. Zane. Which problems ahve strongly exponential complexity? Journal of Computer and System Sciences, 63:512-530, 2001.
19. S. Khot and V. Raman. Parameterized complexity of finding subgraphs with hereditary properties. Theoretical Computer Science, 289:997-1008, 2002.
20. G. Lueker, D. Rose, and R. Tarjan. Algorithmic aspects of vertex elimination in graphs. SIAM Journal on Computing, 5:169-176, 1976.
21. B. Monien. How to find long paths efficiently. Annals of Discrete Mathematics, 25:239-254, 1985.
22. S. D. Nikolopoulos and L. Palios. Hole and antihole detection in graphs. In Proceedings of the 15th Annual ACM-SIAM symposium on Discrete algorithms (SODA '04), 850-859, 2004.
23. C. H. Papadimitriou. Computational Complexity. Addison-Wesley Publishing Company, 1994.
24. C. H. Papadimitriou and M. Yannakakis. On limited nondeterminism and the complexity of the VC-dimension. Journal of Computer and System Sciences, 43:425-440, 1991.
25. J. Plehn and B. Voigt. Finding minimally weighted subgraphs. In R. Möhring, editor, Graph-Theoretic Concepts in Computer Science, WG 90, volume 484 of Lecture Notes in Computer Science, 18-29. Springer-Verlag, 1990.
26. M. Thurley. Tractability and intractability of parameterized counting problems. Diplomarbeit, Humboldt-Universität zu Berlin, 2006.
27. G. Woeginger and J. Sgall. The complexity of coloring graphs without long induced paths. Acta Cybernetica. 15:107-117, 2001.