Embeddings and Ramsey numbers of sparse k-uniform hypergraphs

Details Embeddings and Ramsey numbers of sparse k-uniform hypergraphs Embeddings and Ramsey numbers of sparse k-uniform hypergraphs

2006-12-13

arxiv.org/abs/math/0612351v2

Mathematics

Combinatorics

24 pages, 2 figures. To appear in Combinatorica

Scientific paper

Chvatal, Roedl, Szemeredi and Trotter proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In previous work, we proved the same result for 3-uniform hypergraphs. Here we extend this result to k-uniform hypergraphs, for any integer k > 3. As in the 3-uniform case, the main new tool which we prove and use is an embedding lemma for k-uniform hypergraphs of bounded maximum degree into suitable k-uniform `quasi-random' hypergraphs.

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