Avoiding small subgraphs in Achlioptas processes

Random Structures and Algorithms

Volumn 34, Issue 1, 2009, Pages 165-195

  Krivelevich, Michael ^a   Loh, Po Shen ^b   Sudakov, Benny ^c  

^a TEL AVIV UNIVERSITY   (Israel)

^b PRINCETON UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Achlioptas process; Random graph; Small subgraph; Threshold

Indexed keywords

EID: 59349118531     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20254     Document Type: Article

References (17)

1. N. Alon and J. Spencer, The probabilistic method, 2nd edition, Wiley, New York, 2000.
2. A. Beveridge, T. Bohman, A. Frieze, and O. Pikhurko, Product rule wins a competitive game, Proc Am Math Soc 135 (2007), 3061-3071.
3. A. Beveridge, T. Bohman, A. Frieze, and O. Pikhurko, Memoryless rules for Achlioptas processes, SIAM J Discrete Math, (in press).
4. T. Bohman and A. Frieze, Avoiding a giant component, Random Struct Algorithms 19 (2001), 75-85.
5. T. Bohman, A. Frieze, and N. Wormald, Avoidance of a giant component in half the edge set of a random graph, Random Struct Algorithms 25 (2004), 432-449.
6. T. Bohman and J. Kim, A phase transition for avoiding a giant component, Random Struct Algorithms 28 (2006), 195-214.
7. T. Bohman and D. Kravitz, Creating a giant component, Combinatorics Probab Comput 15 (2006), 489-511.
8. B. Bollobás, Random graphs, 2nd edition, Cambridge studies in advanced mathematics, Vol. 73, Cambridge University Press, Cambridge, 2001.
9. B. Bollobás, Random graphs, In Combinatorics, (Swansea, 1981), London Math. Soc. Lecture Note Ser. Vol. 52, Cambridge University Press, Cambridge, 1981, pp. 80-102.
10. B. Bollobás and A. Thomason, Threshold functions, Combinatorica 7 (1987), 35-38.
11. P. Erdos and A. Rényi, On the evolution of random graphs, Publ Math Inst Hungar Acad Sci 5 (1960), 17-61.
12. P. Erdos and M. Simonovits, Compactness results in extremal graph theory, Combinatorica 2 (1982), 275-288.
13. A. Flaxman, D. Garmanik, and G. Sorkin, Embracing the giant component, Random Struct Algorithms 27 (2005), 277-289.
14. S. Janson, T. Łuczak, and A. Ruciński, Random graphs, Wiley, New York, 2000.
15. T. Köváři, V. Sós, and P. Turán, On a problem of K. Zarankiewicz, Colloquium Math 3 (1954), 50-57.
16. J. Spencer and N. Wormald, Birth control for giants, Combinatorica 27 (2007), 587-628.
17. V. Vu, Concentration of non-Lipschitz functions and applications, Random Struct Algorithms 20 (2002), 262-316.