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Ramsey Properties of Random k-Partite, k-Uniform Hypergraphs

2007; Society for Industrial and Applied Mathematics; Volume: 21; Issue: 2 Linguagem: Inglês

10.1137/060657492

1095-7146

Vojtěch Rödl, Andrzej Ruciński, Mathias Schacht,

Mathematical Dynamics and Fractals

We investigate the threshold probability for the property that every r-coloring of the edges of a random binomial k-uniform hypergraph ${\mathbb G }^{(k)}(n,p)$ yields a monochromatic copy of some fixed hypergraph G. In this paper we solve the problem for arbitrary $k\geq 3$ and k-partite, k-uniform hypergraphs G.