论文信息 - The Ramsey number for hypergraph cycles I

The Ramsey number for hypergraph cycles I

Let Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1.....,vn and edges v1v2v3, v3v4v5, v5v6v7,.....,vn-1vnv1. We prove that every red-blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of Cn, where N is asymptotically equal to 5n/4. Moreover this result is (asymptotically) best possible.

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