A threshold for unsatisfiability
Journal of Computer and System Sciences
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The scaling window of the 2-SAT transition
Random Structures & Algorithms
Sharp threshold and scaling window for the integer partitioning problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
Phase Transitions in Combinatorial Optimization Problems - Basics, Algorithms and Statistical Mechanics
Threshold values of random K-SAT from the cavity method
Random Structures & Algorithms
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The phase transition in inhomogeneous random graphs
Random Structures & Algorithms
The critical phase for random graphs with a given degree sequence
Combinatorics, Probability and Computing
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A new approach to the giant component problem
Random Structures & Algorithms
The probability that a random multigraph is simple
Combinatorics, Probability and Computing
Component structure of the vacant set induced by a random walk on a random graph
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 0.00 |
We consider a random graph on a given degree sequence D, satisfying certain conditions. We focus on two parameters Q = Q(D),R = R(D). Molloy and Reed proved that Q = 0 is the threshold for the random graph to have a giant component. We prove that if |Q| = O(n-1/3R2/3) then, with high probability, the size of the largest component of the random graph will be of order Θ(n2/3R-1/3). If Q is asymptotically larger/smaller that n-1/3R2/3 then the size of the largest component is asymptotically larger/smaller than n2/3R-1/3. In other words, we establish that |Q| = O(n-1/3R2/3) is the scaling window.