Regular subgraphs of random graphs

Random Structures and Algorithms

Volumn 29, Issue 1, 2006, Pages 1-13

  Bollobás, Béla ^a,b   Kim, Jeong Han ^c   Verstraëte, Jacques ^d  

^a University of Memphis   (United States)

^b TRINITY COLLEGE   (United Kingdom)

^c MICROSOFT RESEARCH   (United States)

^d UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745954487     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20123     Document Type: Review

References (27)

1. N. Alon, Combinatorial Nullstellensatz. Recent trends in combinatorics (Mátraháza, 1995), Combin Probab Comput 8(1-2) (1999), 7-29.
2. N. Alon, S. Friedland, and G. Kalai, Regular subgraphs of almost regular graphs, J Combin Theory B 37(1) (1984), 79-91.
3. N. Alon and J. Spencer, The probabilistic method, Second ed., Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York, 2000.
4. R. Baker, G. Harman, and J. Pintz, The difference between consecutive primes. II, Proc London Math Soc 83(3) (2001), 532-562.
5. A. Békéssy, P. Békéssy, and J. Komlós, Asymptotic enumeration of regular matrices, Stud Sci Math Hungar 7 (1972), 343-353.
6. E. Bender and R. Canfield, The asymptotic number of labeled graphs with given degree sequences, J Combinator Theor A 24 (1978), 296-307.
7. J. Bondy and U. Murty, Graph Theory and Applications, MacMillan, London, 1976.
8. B. Bollobás, The evolution of sparse graphs, Graph Theory and Combinatorics (Cambridge 1983), Academic Press, London, 1984, pp. 35-57.
9. B. Bollobás, A probabilistic proof of an asymptotic formula for the number of labelled regular graphs, Eur J Combin 1 (1980), 311-316.
10. B. Bollobás, Random graphs, Second ed., Cambridge Studies in Advanced Mathematics, 73. Cambridge University Press, Cambridge, 2001.
11. B. Bollobás, C. Cooper, T. Fenner, and A. Frieze, Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least k, J Graph Theory 34(1) (2000), 42-59.
12. V. Chvátal, Almost all graphs with 1.44n edges are 3-colorable, Random Struct Algor 2 (1991), 11-28.
13. P. Flajolet, D. Knuth, and B. Pittel, The first cycles in an evolving graph, Discrete Math 75 (1989), 167-215.
14. M. Huxley, On the difference between consecutive primes, Invent Math 15 (1972), 164-170.
15. S. Janson, Poisson convergence and Poisson processes with applications to random graphs, Stochastic Process Appl 26 (1987), 1-30.
16. J-H. Kim, Poisson cloning model for random graph (manuscript can be found in http://research.microsoft.com/research/theory/jehkim/papers/PCMRG.pdf).
17. T. Łuczak, Size and connectivity of the k-core of a random graph, Discrete Math 91(1) (1991), 61-68.
18. M. Molloy, Math, Thesis, University of Waterloo, 1992.
19. M. Molloy and B. Reed, Critical subgraphs of a random graph, Electron J Combin 6 (1999).
20. B. Pittel, J. Spencer, and N. Wormald, Sudden emergence of a giant k-core in a random graph, J Combin Theory B 67(1) (1996), 111-151.
21. L. Pyber, Regular subgraphs of dense graphs, Combinatorica 5(4) (1985), 347-349.
22. L. Pyber, V. Rödl, and E. Szemerédi, Dense graphs without 3-regular subgraphs, J Combin Theory B 63(1) (1995), 41-54.
23. V. Táskinov, Regular subgraphs of regular graphs, Soviet Math Dokl 26 (1982), 37-38.
24. V. Táskinov, Regular parts of regular pseudographs, Mat Zametki 43(2) (1988), 263-275, 303;
25. translation in Math Notes 43(1-2) (1988), 149-156.
26. D. Wilson, On the critical exponents of random k-SAT, Random Struct Algor 21(2) (2002), 182-195.
27. N. Wormald, Models of random regular graphs, Surveys in Combinatorics, Eds. J. D. Lamb and D. A. Preece, 1999, pp. 239-298.