Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
A sharp threshold for k-colorability
Random Structures & Algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Almost all graphs with average degree 4 are 3-colorable
Journal of Computer and System Sciences - STOC 2002
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
On the solution-space geometry of random constraint satisfaction problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A new look at survey propagation and its generalizations
Journal of the ACM (JACM)
The Resolution Complexity of Random Constraint Satisfaction Problems
SIAM Journal on Computing
Reconstruction for Models on Random Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Information, Physics, and Computation
Information, Physics, and Computation
On the random satisfiable process
Combinatorics, Probability and Computing
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Hard and easy distributions of SAT problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
A Better Algorithm for Random $k$-SAT
SIAM Journal on Computing
On the solution-space geometry of random constraint satisfaction problems
Random Structures & Algorithms
The condensation transition in random hypergraph 2-coloring
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The set of solutions of random XORSAT formulae
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On independent sets in random graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On belief propagation guided decimation for random k-SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Going after the k-SAT threshold
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We rigorously determine the exact freezing threshold, rkf, for k-colourings of a random graph. We prove that for random graphs with density above rkf, almost every colouring is such that a linear number of variables are frozen, meaning that their colours cannot be changed by a sequence of alterations whereby we change the colours of o(n) vertices at a time, always obtaining another proper colouring. When the density is below rkf, then almost every colouring has at most o(n) frozen variables. This confirms hypotheses made using the non-rigorous cavity method. It has been hypothesized that the freezing threshold is the cause of the "algorithmic barrier", the long observed phenomenon that when the edge-density of a random graph exceeds hf k ln k(1+ok(1)), no algorithms are known to find k-colourings, despite the fact that this density is only half the k-colourability threshold. We also show that rkf is the threshold of a strong form of reconstruction for k-colourings of the Galton-Watson tree, and of the graphical model.