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Abstract
Chvatal, Rodl, Szemer,di and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [6,23] the same result was proved for 3-uniform hypergraphs. Here we extend this result to kappa-uniform hypergraphs for any integer kappa a parts per thousand yen 3. As in the 3-uniform case, the main new tool which we prove and use is an embedding lemma for kappa-uniform hypergraphs of bounded maximum degree into suitable kappa-uniform 'quasi-random' hypergraphs.
Original language | English |
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Pages (from-to) | 263-297 |
Number of pages | 35 |
Journal | Combinatorica |
Volume | 29 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 May 2009 |
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Dive into the research topics of 'Embeddings and Ramsey numbers of sparse k-uniform hypergraphs'. Together they form a unique fingerprint.Projects
- 1 Finished
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Probabilistic Methods in Graph Theory
Engineering & Physical Science Research Council
26/04/06 → 25/01/09
Project: Research Councils