When does the giant component bring unsatisfiability?

Combinatorica

Volumn 28, Issue 6, 2008, Pages 693-734

  Molloy, Michael ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 65749094850     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-008-2123-5     Document Type: Article

References (39)

1. D. Achlioptas: Setting two variables at a time yields a new lower bound for random 3-SAT, in: Proceedings of the 32nd STOC, (2000), pp. 28-37.
2. D. Achlioptas P. Beame M. Molloy 2004 A sharp threshold in proof complexity yields a lower bound for satisfiability search J. Comp. Sys. Sci. 68 2 238 268
3. D. Achlioptas, A. Chtcherba, G. Istrate and C. Moore: The phase transition in NAESAT and 1-in-k SAT, in: Proceedings of SODA, (2001), pp. 721-722.
4. D. Achlioptas E. Friedgut 1999 A threshold for k-colourability Random Structures and Algorithms 14 63 70
5. D. Achlioptas L. Kirousis E. Kranakis D. Krizanc M. Molloy Y. Stamatiou 2001 Random constraint satisfaction: a more accurate picture Constraints 6 4 329 344
6. D. Achlioptas and M. Molloy: Analysis of a list-coloring algorithm on a random graph, in: Proceedings of the 38th FOCS, (1997), pp. 204-212.
7. D. Achlioptas and M. Molloy: Almost all graphs with 2.522n edges are not 3-colorable, Electronic Journal of Combinatorics 6(1) (1999), #R29. (Pubitemid 39605679)
8. D. Achlioptas C. Moore 2006 Random k-SAT: Two moments suffice to cross a sharp threshold SIAM J. Comput. 36 740 762 (Pubitemid 46976573)
9. D. Achlioptas C. Moore 2003 Almost all graphs with average degree 4 are 3-colorable J. Comp. Sys. Sci. 67 2 441 471
10. D. Achlioptas and G. B. Sorkin: Optimal myopic algorithms for random 3-SAT, in: Proceedings of the 41st FOCS, (2000), 590-600.
11. P. Beame R. Karp T. Pitassi M. Saks 2002 The efficiency of resolution and Davis-Putnam procedures SIAM J. Comput. 31 1048 1075
12. B. Bollobás: Random Graphs, Academic Press, London, 1985.
13. B. Bollobás C. Borgs J. T. Chayes J. H. Kim D. B. Wilson 2001 The scaling window of the 2-SAT transition Random Structures and Algorithm 18 201 256 (Pubitemid 33269969)
14. V. Chvátal and B. Reed: Mick gets some (the odds are on his side), in: Proceedings of the 33rd FOCS, (1992), pp. 620-627.
15. V. Chvátal E. Szemerédi 1988 Many hard examples for resolution Journal of the ACM 35 759 768
16. N. Creignou H. Daude 2003 Generalized satisfiability problems: minimal elements and phase transitions Th. Comp. Sci. 302 417 430
17. N. Creignou H. Daude 2004 Combinatorial sharpness criterion and phase transition classification for random CSP's Information and Computation 190 220 238
18. O. Dubois and J. Mandler: On the non-3-colourability of random graphs, arXiv:math/0209087.
19. O. Dubois, Y. Boufkhad and J. Mandler: Typical random 3-SAT formulae and the satisfiability threshold, in: Proceedings of the 11th SODA, (2000), pp. 126-127. (Pubitemid 30549252)
20. P. Erdos A. Rényi 1960 On the evolution of random graphs Mat. Kutató Int. Közl. 5 17 60
21. W. Fernandex de la Vega: On random 2-SAT, manuscript (1992).
22. N. Fountoulakis C. [tmp] McDiarmid 2002 Upper bounds on the non-3-colourability threshold of random graphs Discrete Math. & Th. Comp. Sci. 5 1 205 226
23. E. Friedgut 1999 Sharp thresholds of graph properties and the k-SAT problem J. Am. Math. Soc. 12 1017 1054
24. I. Gent E. [tmp] MacIntyre P. Prosser B. Smith T. Walsh 2001 Random constraint satisfaction: flaws and structure Constraints 6 345 372
25. A. Goerdt 1996 A threshold for unsatisfiability J. Comp. Sys. Sci. 53 469 486 (Pubitemid 126653479)
26. G. Istrate 2005 Threshold properties of random boolean constraint satisfaction problems Disc. Appl. Math. 153 1-3 141 152
27. H. Hatami M. Molloy 2008 Sharp thresholds for constraint satisfaction problems and homomorphisms Random Structures and Algorithms 33 3 310 332
28. S. Janson, T. Łuczak and A. Ruciński: Random Graphs, Wiley, New York (2000).
29. S. Janson Y. Stamatiou M. Vanvakari 2000 Bounding the unsatisfiability threshold of random 3-SAT Random Structures and Algorithms 17 103 116
30. R. Karp 1990 The transitive closure of a random digraph Random Structures and Algorithms 1 73 94
31. A. Kaporis L. Kirousis E. Lalas 2006 The probabilistic analysis of a greedy satisfiability algorithm Random Structures and Algorithms 28 4 444 480
32. A. Kaporis, L. Kirousis and Y. Stamatiou: A note on the non-colourability threshold of a random graph, Electronic J. Comb. 7 (2000), #R29. (Pubitemid 39064728)
33. L. Kirousis E. Kranakis D. Krizanc Y. Stamatiou 1998 Approximating the unsatisfiability threshold of random formulas Random Structures and Algorithms 12 253 269 (Pubitemid 128444540)
34. T. Łuczak M. Karonski 2002 The phase transition in a random hypergraph J. Comput. Appl. Math. 142 125 135 (Pubitemid 34519909)
35. D. Mitchell: Resolution complexity of random constraints, in: Proceedings of Principles and Practice of Constraint Programming - CP, (2002), pp. 295-309.
36. M. Molloy 2003 Models for random constraint satisfaction problems SIAM J. Comput. 32 4 935 949
37. M. Molloy M. Salavatipour 2007 The resolution complexity of random constraint satisfaction problems SIAM J. Comput. 37 3 895 922
38. R. Monasson R. Zecchina S. Kirkpatrick B. Selman L. Troyansky 1999 Determining computational complexity from characteristic 'phase transitions' Nature 400 8 133 137 (Pubitemid 29327535)
39. D. S. Passman: Permutation Groups, Benjamin, New York (1968).