Cores in random hypergraphs and Boolean formulas

Random Structures and Algorithms

Volumn 27, Issue 1, 2005, Pages 124-135

  Molloy, Michael ^a,b  

^a UNIVERSITY OF TORONTO   (Canada)

^b MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24144432057     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.20061     Document Type: Article

References (24)

1. D. Achlioptas, Lower bounds for random 3-SAT via differential equations, Theoret Comput Sci 265(1-2) (2001), 159-185.
2. rd Symp Theory Comput (STOC), 2001, pp. 337-346.
3. D. Achlioptas and M. Molloy, Analysis of a list-colouring algorithm on a random graph, Proc 38th Annu Symp Foundations of Computer Science (FOCS), 1997, pp. 204-212.
4. K. Azuma, Weighted sums of certain dependent random variables, Tokuku Math J 19 (1967), 357-367.
5. E. A. Bender and E. R. Canfield, The asymptotic number of labelled graphs with given degree sequences, J Combinat Theory Ser A 24 (1978), 296-307.
6. B. Bollobás. "The evolution of sparse graphs" Graph theory and combinatorics, Ed., B. Bollobás, Academic Press, Boston, 1984, pp. 35-57.
7. B. Bollobás, Martingales, isoperimetric inequalities and random graphs, Colloq Math Soc Janós Bolyai 52 (1987), 113-139.
8. B. Bollobás and G. Brightwell, The width of random graph orders, Math Sci 20 (1995), 69-90.
9. A. Broder, A. Frieze, and E. Upfal, On the satisfiability and maximum satisfiability of random 3-CNF formulas, Proc 4th Annu ACM-SIAM Symp Discrete Algorithms (SODA), 1993, pp. 322-330.
10. V. Chvátal, Almost all graphs with 1.44n edges are 3-colourable, Random Structures Algorithms 2 (1991), 11-28.
11. V. Chvátal and E. Szemeredi, Many hard examples for resolution, J ACM 35 (1988), 759-768.
12. C. Cooper, A. Frieze, M. Molloy, and B. Reed, Perfect matchings in random r-regular, s-uniform hypergraphs, Combinat Probab Comput 5 (1996), 1-14.
13. P. Erdös and A. Rényi, On the evolution of random graphs, Magayr Tud Akad Mat Kutato Int Kozl 5 (1960), 17-61.
14. D. Fernholz and V. Ramachandran, Cores and connectivity in sparse random graphs, Technical Report TR-04-13, The University of Texas at Austin, Department of Computer Sciences, 2004.
15. A. Goerdt and M. Molloy, Analysis of edge deletion processes on random regular graphs, Theoret Comput Sci 297 (2003), 241-260.
16. B. Majewski, N. Wormald, G. Havas, and Z. Czech, A family of perfect hashing methods, Comput J 39(6) (1996), 547-554.
17. S. Janson, T. Luczak, and A. Ruciński, Random graphs, Wiley, New York, 2000.
18. J. Kim, Poisson cloning model for random graphs, in preparation.
19. M. Luby, M. Mitzenmacher, and A. Shokrollahi, Analysis of random processes via and-or tree evaluation, Proc 9th Symp Discrete Algorithms (SODA), 1998, pp. 364-373.
20. T. Luczak, Size and connectivity of the k-core of a random graph, Discrete Math 91 (1991), 61-68.
21. M. Mitzenmacher, Tight thresholds for the pure literal rule, Technical Note 1997-011, Digital Systems Research Center, Palo Alto, CA 1997.
22. M. Molloy, A gap between the appearance of a k-core and a k-chromatic graph, Random Structures Algorithms 8 (1996), 159-160.
23. B. Pittel, J. Spencer, and N. Wormald, Sudden emergence of a giant k-core in a random graph, J Combinat Theory Ser B 67 ( 1996), 111-151.
24. N. C. Wormald, Some problems in the enumeration of labelled graphs, Doctoral thesis, Newcastle University, 1978.