The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. J. Balogh, B. G. Pittel, Bootstrap percolation on the random regular graph. Random Structures Algorithms 30 (2007), no. 1-2, 257--286. MR2283230
  2. B. Bollobás, The evolution of sparse graphs. Graph theory and Combinatorics (Cambridge, 1983), 35--57, Academic Press, London, 1984. MR0777163
  3. B. Bollobás, Random Graphs, 2nd ed., Cambridge Univ. Press, Cambridge, 2001. MR1864966
  4. T. Britton, S. Janson and A. Martin-Löf, Graphs with specified degree distributions, simple epidemics and local vaccination strategies. Advances Appl. Probab. 39 (2007), no. 4, 922--948. MR2381582
  5. J. Cain and N. Wormald, Encore on cores. Electronic J. Combinatorics, 13 (2006), no. 1, R81. MR2255423
  6. R. W. R. Darling, D. A. Levin and J. R. Norris, Continuous and discontinuous phase transitions in hypergraph processes. Random Structures Algorithms 24 (2004), no. 4, 397--419. MR2060628
  7. N. Fountoulakis, Percolation on sparse random graphs with given degree sequence. Preprint, 2007. arXiv:math/0703269v1
  8. A. Gut, Probability: A Graduate Course. Springer, New York, 2005. MR2125120
  9. S. Janson, The probability that a random multigraph is simple. Combin. Probab. Comput., to appear. arXiv:math.CO/0609802
  10. S. Janson and M. J. Luczak, A simple solution to the k-core problem. Random Structures Algorithms 30 (2007), no. 1-2, 50--62. MR2283221
  11. S. Janson and M. J. Luczak, Asymptotic normality of the k-core in random graphs. Ann. Appl. Probab., 18 (2008), no. 3, 1085--1137. MR2418239
  12. S. Janson and M. J. Luczak, A new approach to the giant component problem. Random Structures Algorithms, to appear. arXiv:0707.1786v1
  13. O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer, New York, 2002. MR1876169
  14. T. Luczak, Size and connectivity of the k-core of a random graph, Discr. Math. 91 (1991) 61--68. MR1120887
  15. M. Molloy and B. Reed, A critical point for random graphs with a given degree sequence, Random Structures Algorithms 6 (1995), no. 2--3, 161--179. MR1370952
  16. M. Molloy and B. Reed, The size of the giant component of a random graph with a given degree sequence, Combin. Probab. Comput. 7 (1998), no. 3, 295--305. MR1664335
  17. B. Pittel, J. Spencer and N. Wormald, Sudden emergence of a giant k-core in a random graph, J. Combin. Theor. Ser. B 67 (1996), 111--151. MR1385386
  18. O. Riordan, The k-core and branching processes. Combin. Probab. Comput. 17 (2008), no. 1, 111--136. MR2376426
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.