NP-completeness results for edge modification problems

Discrete Applied Mathematics

Volumn 154, Issue 13 SPEC. ISS., 2006, Pages 1824-1844

  Burzyn, Pablo ^a   Bonomo, Flavia ^a   Durán, Guillermo ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

Computational complexity; Edge modification problems; Graph classes; NP completeness

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY; SET THEORY; THEOREM PROVING;

EDGE MODIFICATION PROBLEMS; GRAPH CLASSES; NP-COMPLETENESS;

PROBLEM SOLVING;

EID: 33745837828     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.03.031     Document Type: Article

References (36)

1. Bodlaender H., and De Fluiter B. On intervalizing k-colored graphs for DNA physical mapping. Discrete Appl. Math. 71 (1966) 55-77
2. F. Bonomo, G. Durán, M. Groshaus, Coordinated graphs and clique graphs of clique-Helly perfect graphs, Utilitas Mathematica, to appear.
3. Booth K., and Lueker G. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Sci. Technol. 13 (1976) 335-379
4. Brandstädt A., Le V., and Spinrad J. Graph Classes: A Survey (1999), SIAM, Philadelphia
5. Burzyn P., Bonomo F., and Durán G. Computational complexity of edge modification problems in different classes of graphs. Electron. Notes Discrete Math. 18 (2004) 41-46
6. Chudnovsky M., Cornuéjols G., Liu X., Seymour P., and Vušković K. Recognizing Berge Graphs. Combinatorica 25 (2005) 143-187
7. Deng X., Hell P., and Huang J. Linear time representation algorithms for proper circular-arc graphs and proper interval graphs. SIAM J. Comput. 25 (1996) 390-403
8. Durán G. Some new results on circle graphs. Matemática Contemporânea 25 (2003) 91-106
9. Durán G., Gravano A., McConnell R., Spinrad J., and Tucker A. Polynomial time recognition of unit circular-arc graphs. J. Algorithms 58 (2006) 67-78
10. Durán G., and Lin M. Clique graphs of Helly circular-arc graphs. Ars Combinatoria 60 (2001) 255-271
11. Dushnik B., and Miller E. Partially ordered sets. Amer. J. Math. 63 (1941) 600-610
12. El-Mallah E., and Colbourn C. The complexity of some edge deletion problems. IEEE Trans. Circuits Systems 35 3 (1988) 354-362
13. Farber M., and Jamison R. On local convexity in graphs. Discrete Math. 66 (1987) 231-247
14. Garey M., and Johnson D. Computers and Intractability: A Guide to the Theory of NP-Completeness (1979), Freeman and Company, San Francisco
15. Garey M., Johnson D., and Stockmeyer L. Some simplified NP-complete graph problems. Theoret. Comput. Sci. 1 3 (1976) 237-267
16. Goldberg P., Golumbic M., Kaplan H., and Shamir R. Four strikes against physical mapping of DNA. J. Comput. Biol. 2 (1995) 139-152
17. Golumbic M. Algorithmic Graph Theory and Perfect Graphs (1980), Academic Press, New York
18. Golumbic M., Kaplan H., and Shamir R. On the complexity of DNA physical mapping. Adv. in Appl. Math. 15 (1994) 251-261
19. M. Groshaus, J. Szwarcfiter, Bichromatic cliques, bicliques: the Helly property, manuscript, 2004.
20. Hakimi S., Schmeichel E., and Young N. Orienting graphs to optimize reachability. Inform. Process. Lett. 63 (1997) 229-235
21. Hammer P., and Simeone B. The splittance of a graph. Combinatorica 1 (1981) 275-284
22. Lekkerkerker C., and Boland D. Representation of finite graphs by a set of intervals on the real line. Fundamenta Mathematicae 51 (1962) 45-64
23. Margot F. Some complexity results about threshold graphs. Discrete Appl. Math. 49 (1994) 229-308
24. McConnell R. Linear-time recognition of circular-arc graphs. Algorithmica 37 2 (2003) 93-147
25. R. McConnell, J. Spinrad, Linear-time transitive orientation, Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, 1997, pp. 19-25.
26. Natanzon A., Shamir R., and Sharan R. Complexity classification of some edge modification problems. Discrete Appl. Math. 113 (2001) 109-128
27. E. Prisner, Bicliques in Graphs II: Recognizing k-Path Graphs and Underlying Graphs of Line Digraphs, Lecture Notes in Computer Science, vol. 1335, 1997, pp. 273-287.
28. Prisner E. Bicliques in graphs I: bounds on their number. Combinatorica 20 1 (2000) 109-117
29. Rose J. A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations. In: Reed R.C. (Ed). Graph Theory and Computing (1972), Academic Press, New York 183-217
30. R. Sharan, Graph modification problems and their applications to genomic research, Ph.D. Thesis, Sackler Faculty of Exact Sciences, School of Computer Science, Tel-Aviv University, Tel-Aviv, 2002.
31. Spinrad J. Recognition of circle graphs. J. Algorithms 16 2 (1994) 264-282
32. Spinrad J., and Sritharan R. Algorithms for weakly triangulated graphs. Discrete Appl. Math. 59 (1995) 181-191
33. Szwarcfiter J. Recognizing clique-Helly graphs. Ars Combinatoria 45 (1997) 29-32
34. Szwarcfiter J., and Bornstein C. Clique graphs of chordal and path graphs. SIAM J. Discrete Math. 7 (1994) 331-336
35. Yannakakis M. Computing the minimum fill-in is NP-complete. SIAM J. Algebraic Discrete Methods 2 1 (1981) 77-79
36. Yannakakis M. Edge deletion problems. SIAM J. Comput. 10 2 (1981) 297-309