Creation and growth of components in a random hypergraph process

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4112 LNCS, Issue , 2006, Pages 350-359

  Ravelomanana, Vlady ^a   Rijamamy, Alphonse Laza ^b  

^a CNRS   (France)

^b Centre de recherche pour le développement   (Madagascar)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; PHASE TRANSITIONS; PROBABILITY;

RANDOM HYPERGRAPH PROCESS;

RANDOM PROCESSES;

EID: 33749575872     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11809678_37     Document Type: Conference Paper

References (20)

1. Andriamampianina T. and Ravelomanana V. (2005). Enumeration of connected uniform hypergraphs. In Proc. of the 17-th Formal Power Series and Algebraic Combinatorics.
2. Berge, C. (1976). Graphs and hypergraphs North-Holland Mathematical Library.
3. Bergeron, F., Labelle, G. and Leroux, P. (1998). Combinatorial Species and Tree-like Structures Encyclopedia of Mathematics and its Applications, Vol. 67, Cambridge Univ. Press.
4. Bollobás, B. (1985) Random Graphs Academic Press, London.
5. De Bruijn, N. G. (1981). Asymptotic Methods in Analysis. Dover, New-York.
6. Coja-Oghlan, A., Moore, C. and Sanwalani, V. (2004). Counting Connected Graphs and Hypergraphs via the Probabilistic Method. In Proc. of APPROX-RANDOM 2004.
7. Flajolet, P. and Sedgewick, R. Analytic Combinatorics. To appear (chapters are avalaible as Inria research reports). See http://falgo.inria.fr/ flajolet/Publications/books.html.
8. Harary, F. and Palmer, E. (1973). Graphical Enumeration. Academic Press, New-York and London.
9. Herbert S. Wilf Generatingfunctionology
10. Janson, S. (1993). Multicyclic components in random graphs process. Random Structures and Algorithms, 4:71-84.
11. Janson, S. (2000). Growth of components in random graphs. Random Structures and Algorithms, 17:343-356.
12. Janson, S., Knuth, D. E., Luczak, T. and Pittel B. (1993). The birth of the giant component. Random Structures and Algorithms, 4:233-358.
13. Janson, S., Luczak, T. and Rucinski A. (2000). Random Graphs. John Wiley, New York.
14. Karonski, M. and Luczak, T. (1997). The number of sparsely edges connected uniform hypergraphs. Discrete Math. 171:153-168.
15. Karonski, M. and Luczak, T. and (2002). The phase transition in a random hypergraph. J. Comput. Appl. Math. 142:125-135.
16. Knuth, D. E. and Pittel, B. (1989). A recurrence related to trees. Proc. Am. Math. Soc., 105:335-349.
17. Ravelomanana, V. (to appear). The average size of giant components between the double-jump. Algorithmica.
18. Schmidt-Pruznan, J. and Shamir S. (1985). Component structure in the evolution of random hypergraphs Combinatorica 5: 81-94.
19. Wright, E. M. (1977). The Number of Connected Sparsely Edged Graphs. Journal of Graph Theory, 1:317-330.
20. Wright, E. M. (1980). The Number of Connected Sparsely Edged Graphs. III. Asymptotic results Journal of Graph Theory, 4:393-407.