Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
The isoperimetric number of random regular graphs
European Journal of Combinatorics
The first cycles in an evolving graph
Discrete Mathematics
A guided tour of Chernoff bounds
Information Processing Letters
Uniform generation of random regular graphs of moderate degree
Journal of Algorithms
Size and connectivity of the k-core of a random graph
Discrete Mathematics
On the independence and chromatic numbers of random regular graphs
Journal of Combinatorial Theory Series B
Randomized algorithms
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 threshold for unsatisfiability
Journal of Computer and System Sciences
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete 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
Random 2-SAT: results and problems
Theoretical Computer Science - Phase transitions in combinatorial problems
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimum independent dominating sets of random cubic graphs
Random Structures & Algorithms
Talagrand's Inequality and Locality in Distributed Computing
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
New Spectral Lower Bounds on the Bisection Width of Graphs
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Small maximal matchings in random graphs
Theoretical Computer Science - Latin American theoretical informatics
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Bounds on the max and min bisection of random cubic and random 4-regular graphs
Theoretical Computer Science - Selected papers in honor of Lawrence Harper
Almost all graphs with average degree 4 are 3-colorable
Journal of Computer and System Sciences - STOC 2002
Random Regular Graphs of Non-Constant Degree: Connectivity and Hamiltonicity
Combinatorics, Probability and Computing
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
On the Independent Domination Number of Random Regular Graphs
Combinatorics, Probability and Computing
A simple solution to the k-core problem
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
Colouring Random 4-Regular Graphs
Combinatorics, Probability and Computing
Bounds on the bisection width for random d -regular graphs
Theoretical Computer Science
The k-core and branching processes
Combinatorics, Probability and Computing
Acyclic edge colorings of graphs
Journal of Graph Theory
Maximum matching in sparse random graphs
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
The acyclic edge chromatic number of a random d-regular graph is d + 1
Journal of Graph Theory
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
On the satisfiability threshold and clustering of solutions of random 3-SAT formulas
Theoretical Computer Science
On the chromatic number of a random 5-regular graph
Journal of Graph Theory
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
On the satisfiability threshold of formulas with three literals per clause
Theoretical Computer Science
Large independent sets in random regular graphs
Theoretical Computer Science
Random Formulas Have Frozen Variables
SIAM Journal on Computing
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We survey several applications of the differential equation method in different areas of discrete mathematics. We give examples of its use in the analysis of algorithms in random graph processes and random Boolean formulae. We also briefly review the basic theorem of Wormald (1999) [1] used in the analysis, but we aim for simplicity and not for maximal generality. The primary goal of this survey is to be a toolbox for the usage of the differential equation method.