Name
Abstract | ||
|---|---|---|
Chvátal, Rödl, Szemerédi and Trotter [V. Chvátal, V. Rödl, E. Szemerédi and W.T. Trotter, The Ramsey number of a graph with a bounded maximum degree, J. Combinatorial Theory B 34 (1983), 239–243] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [O. Cooley, N. Fountoulakis, D. Kühn and D. Osthus, 3-uniform hypergraphs of bounded degree have linear Ramsey numbers, submitted] and [B. Nagle, S. Olsen, V. Rödl and M. Schacht, On the Ramsey number of sparse 3-graphs, preprint] the same result was proved for 3-uniform hypergraphs. In [O. Cooley, N. Fountoulakis, D. Kühn and D. Osthus, Embeddings and Ramsey numbers of sparse k-uniform hypergraphs, submitted] we extended this result to k-uniform hypergraphs for any integer k≥3. As in the 3-uniform case, the main new tool which we proved and used is an embedding lemma for k-uniform hypergraphs of bounded maximum degree into suitable k-uniform ‘quasi-random’ hypergraphs. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.endm.2007.07.006 | Electronic Notes in Discrete Mathematics |
Keywords | Field | DocType |
Ramsey numbers,hypergraphs,Regularity lemma | Ramsey theory,Integer,Discrete mathematics,Combinatorics,Embedding,Constraint graph,Ramsey's theorem,Degree (graph theory),Lemma (mathematics),Mathematics,Bounded function | Journal |
Volume | ISSN | Citations |
29 | 1571-0653 | 0 |
PageRank | References | Authors |
0.34 | 6 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniela Kühn | 1 | 463 | 42.11 |
| Oliver Cooley | 2 | 39 | 9.15 |
| Nikolaos Fountoulakis | 3 | 185 | 18.04 |
| Deryk Osthus | 4 | 643 | 76.03 |