Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
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 sharp threshold for k-colorability
Random Structures & Algorithms
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
New methods to color the vertices of a graph
Communications of the ACM
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Studying Balanced Allocations with Differential Equations
Combinatorics, Probability and Computing
Maximum matching in sparse random graphs
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
On the critical exponents of random k-SAT
Random Structures & Algorithms
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
The resolution complexity of random graphk-colorability
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
A novel giant-subgraph phase-transition in sparse random k-partite graphs
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
Hiding satisfying assignments: two are better than one
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Generating hard satisfiable formulas by hiding solutions deceptiveily
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Hiding satisfying assignments: two are better than one
Journal of Artificial Intelligence Research
Generating hard satisfiable formulas by hiding solutions deceptively
Journal of Artificial Intelligence Research
A novel giant-subgraph phase-transition in sparse random k-partite graphs
Discrete Applied Mathematics
The resolution complexity of random graph k-colorability
Discrete Applied Mathematics
Why almost all k-colorable graphs are easy
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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The technique of using differential equations to approximate the mean path of Markov chains has proved very useful in the average-case analysis of algorithms. Here, we significantly expand the range of this technique, by showing that it can be used to handle algorithms that favor high-degree vertices. In particular, we consider the problem of 3-coloring sparse random graphs and analyze a "smoothed" version of the Brelaz heuristic. This allows us to prove that i) almost all graphs with average degree d, i.e. G(n,p=d/n), are 3-colorable for d&xie; 4.03, and that ii) almost all 4-regular graphs are 3-colorable. This improves over the previous lower bound of 3.847 for the G(n,p) 3-colorability threshold and gives the first non trivial result on the 3-colorability of random regular graphs.