Embeddings and Ramsey numbers of sparse k-uniform hypergraphs

Cooley, Oliver; Fountoulakis, Nikolaos; Kühn, Daniela; Osthus, Deryk

Embeddings and Ramsey numbers of sparse k-uniform hypergraphs

Authors

Cooley, Oliver

Fountoulakis, Nikolaos

Kühn, Daniela

Osthus, Deryk

Description

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.
24 pages, 2 figures. To appear in Combinatorica