Improved bounds and algorithms for hypergraph 2-coloring
Random Structures & Algorithms
Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Two-coloring random hypergraphs
Random Structures & Algorithms
How many random edges make a dense graph Hamiltonian?
Random Structures & Algorithms
On the 2-Colorability of Random Hypergraphs
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Adding random edges to dense graphs
Random Structures & Algorithms
On smoothed analysis in dense graphs and formulas
Random Structures & Algorithms
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We study a model of random uniform hypergraphs, where a random instance is obtained by adding random edges to a large hypergraph of a given density. The research on this model for graphs has been started by Bohman et al. (Random Struct Algorithms 22 (2003) 33–42), and continued in (Bohman et al., Random Struct Algorithms 24 (2004) 105–117) and (Krivelevich et al., Random Struct Algorithms 29 (2006), 180–193). Here we obtain a tight bound on the number of random edges required to ensure non-2-colorability. We prove that for any k-uniform hypergraph with Ω(nk-ε) edges, adding ω(nkε-2) random edges makes the hypergraph almost surely non-2-colorable. This is essentially tight, since there is a 2-colorable hypergraph with Ω(nk-ε) edges which almost surely remains 2-colorable even after adding o(nkε-2) random edges.© 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008