The order of the giant component of random hypergraphs

Random Structures and Algorithms

Volumn 36, Issue 2, 2010, Pages 149-184

  Behrisch, Michael ^a   Coja Oghlan, Amin ^b   Kang, Mihyun ^c  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Giant component; Limit theorems; Random graphs and hypergraphs

Indexed keywords

EID: 74349121387     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20282     Document Type: Article

References (24)

1. N. Alon and J. Spencer, The probabilistic method, 2nd edition, New York, 2000.
2. T. Andriamampianina and V. Ravelomanana, Enumeration of connected uniform hypergraphs, Proceedings of FPSAC, Taormina, Italy, 2005.
3. D. Barraez, S. Boucheron, and W. Fernandez de la Vega, On the fluctuations of the giant component, Combinatorics Probability Computing 9 (2000), 287-304.
4. M. Behrsich, Stochastical models for networks in the life sciences, PhD thesis, Berlin, 2007.
5. E. A. Bender, E. R. Canfield, and B. D. McKay, The asymptotic number of labeled connected graphs with a given number of vertices and edges, Random Struc Algorithms 1 (1990), 127-169.
6. B. Bollobás, Random graph, 2nd edition, Cambridge University Press, Cambridge, 2001.
7. A. Coja-Oghlan, C. Moore, and V. Sanwalani, Counting connected graphs and hypergraphs via the probabilistic method, Random Struct Algorithms 31 (2007), 288-329.
8. R. Durrett, Probability and examples, 3rd edition, Brooks/Cole, Belmont, CA, 2005.
9. R. Durrett, Random graph dynamics, Cambridge University Press, Cambridge, 2007.
10. P. Erdos and A. Rényi, On the evolution of random graphs, Publ Math Inst Hung Acad Sci 5 (1960),17-61.
11. R. van der Hofstad and J. Spencer, Counting connected graphs asymptotically, Eur J Combinatorics 27 (2006), 1294-1320.
12. S. Janson, The minimal spanning tree in a complete graph and a functional limit theorem for trees in a random graph, Random Struct Algorithms 7 (1995), 337-355.
13. S. Janson, T. Łuczak, and A. Rucinski, Random graphs, Wiley, New York, 2000.
14. M. Karonski and T. Łuczak, The number of connected sparsely edged uniform hypergraphs, Discrete Math 171 (1997), 153-168.
15. M. Karonski and T. Łuczak, The phase transition in a random hypergraph, J Comput Appl Math 142 (2002), 125-135.
16. N. O'Connell, Some large deviation results for sparse random graphs, Probab Theory Relat Field 110 (1998), 277-285.
17. B. Pittel, On tree census and the giant component in sparse random graphs, Random Struct Algorithms 1 (1990), 311-342.
18. B. Pittel and N. C. Wormald, Counting connected graphs inside out, J Combin Theory Ser B 93 (2005),127-172.
19. A. A. Puhalskii, Stochastic processes in random graphs, Ann Probab 33 (2005), 337-412.
20. V. Ravelomanana, The average size of giant components between the double-jump, Algorithmica 46 (2006), 529-555.
21. V. Ravelomanana and A. L. Rijamamy, Creation and growth of components in a random hypergraph process, preprint (2005).
22. J. Schmidt-Pruzan and E. Shamir, Component structure in the evolution of random hypergraphs, Combinatorica 5 (1985), 81-94.
23. C. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent variables, In Proceedings 6th Berkeley Symposium on Mathematical Statistics and Probability, 1970, pp. 583-602.
24. m(t), Theory Prob App 15 (1970), 55-67.