A sharp threshold for network reliability

Combinatorics Probability and Computing

Volumn 11, Issue 5, 2002, Pages 465-474

  Krivelevich, Michael ^a   Sudakov, Benny ^b,c   Vu, Van H ^d,e  

^a TEL AVIV UNIVERSITY   (Israel)

^b PRINCETON UNIVERSITY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

^d MICROSOFT RESEARCH   (United States)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; GRAPH THEORY; RANDOM PROCESSES; THEOREM PROVING;

CONNECTIVITY THRESHOLD; RANDOM SUBGRAPH;

PROBABILITY DISTRIBUTIONS;

EID: 0036025696     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548302005199     Document Type: Article

References (10)

1. Alon, N. (1995) A note on network reliability. In Discrete Probability and Algorithms (D. Aldous et al., eds), Vol. 72 of IMA Volumes in Mathematics and its Applications, Springer, pp. 11-14.
2. Bollobás, B. (1985) Random Graphs, Academic Press, London.
3. Friedgut, E. (1999) Sharp thresholds of graph properties, and the k-sat problem; with an appendix by Jean Bourgain. J. Amer. Math. Soc. 12 1017-1054.
4. Grimmett, G. (1989) Percolation, Springer.
5. Lovász, L. (1993) Combinatorial Problems and Exercises, North-Holland, Amsterdam.
6. Margulis, G. (1974) Probabilistic characteristics of graphs with large connectivity. Problems Info. Transmission 10 101-108.
7. Pak, I. and Vu, V. (2001) On mixing of certain random walks, cutoff phenomenon and sharp threshold of random matroid processes. Discrete Appl. Math. 110 251-272.
8. Roberts, F., Hwang, F. and Monma, C., eds (1989) Reliability of Computer and Communication Networks, Vol. 5 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science.
9. Talagrand, M. (1993) Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem. Geometric and Functional Analysis 3 295-314.
10. Welsh, D. J. A. (1976) Matroid Theory, Vol. 8 of Lond. Math. Soc. Monographs, Academic Press, London.