Random Structures & Algorithms
Avoidance of a giant component in half the edge set of a random graph
Random Structures & Algorithms
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Random Structures & Algorithms
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Random Structures & Algorithms
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APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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Sharp load thresholds for cuckoo hashing
Random Structures & Algorithms
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Let c be a constant and (e1,f1),(e2,f2),…,(ecn,fcn) be a sequence of ordered pairs of edges from the complete graph Kn chosen uniformly and independently at random. We prove that there exists a constant c2 such that if c c2, then whp every graph which contains at least one edge from each ordered pair (ei,fi) has a component of size Ω(n), and, if c c2, then whp there is a graph containing at least one edge from each pair that has no component with more than O(n1-ε vertices, where ε is a constant that depends on c2 - c. The constant c2 is roughly 0.97677. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006