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On the Ramsey Number of Sparse 3-Graphs |
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| Authors: | Brendan Nagle Sayaka Olsen Vojtěch Rödl Mathias Schacht |
| Institution: | 1. Department of Mathematics, University of South Florida, Tampa, FL, 33620, USA 2. Department of Mathematics and Statistics, University of Nevada, Reno, NV, 89557, USA 3. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA 4. Institut für Informatik, Humboldt-Universit?t zu Berlin, D-10099, Berlin, Germany |
| Abstract: | We consider a hypergraph generalization of a conjecture of Burr and Erd?s concerning the Ramsey number of graphs with bounded degree. It was shown by Chvátal, Rödl, Trotter, and Szemerédi The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory Ser. B 34 (1983), no. 3, 239–243] that the Ramsey number R(G) of a graph G of bounded maximum degree is linear in |V(G)|. We derive the analogous result for 3-uniform hypergraphs. |
| Keywords: | Ramsey theory hypergraphs Burr– Erdő s conjecture |
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