On the independence number of random graphs
Discrete Mathematics
An improved upper bound on the non-3-colourability threshold
Information Processing Letters
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Survey: The cook-book approach to the differential equation method
Computer Science Review
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We look at the minimal size of a maximal matching in general, bipartite and d-regular random graphs. We prove that with high probability the ratio between the sizes of any two maximal matchings approaches one in dense random graphs and random bipartite graphs. Weaker bounds hold for sparse random graphs and random d-regular graphs. We also describe an algorithm that with high probability finds a matching of size strictly less than n/2 in a cubic graph. The result is based on approximating the algorithm dynamics by a number of systems of linear differential equations.