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On the Ramsey Number of Sparse 3-Graphs

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Abstract

We consider a hypergraph generalization of a conjecture of Burr and Erdős 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.

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Authors and Affiliations

  1. Department of Mathematics, University of South Florida, Tampa, FL, 33620, USA

    Brendan Nagle

  2. Department of Mathematics and Statistics, University of Nevada, Reno, NV, 89557, USA

    Sayaka Olsen

  3. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Vojtěch Rödl

  4. Institut für Informatik, Humboldt-Universität zu Berlin, D-10099, Berlin, Germany

    Mathias Schacht

Authors
  1. Brendan Nagle
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  2. Sayaka Olsen
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  3. Vojtěch Rödl
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  4. Mathias Schacht
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Corresponding author

Correspondence to Mathias Schacht.

Additional information

Received: October 4, 2006. Final version received: February 29, 2008.

Brendan Nagle: Author was partially supported by NSF grant DMS 0639839.

Sayaka Olsen: Author was partially supported by NSF award EPS 0132556.

Vojtěch Rödl: Author was partially supported by NSF grant DMS 0300529.

Mathias Schacht: Author was supported by DFG grant SCHA 1263/1–1.

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Nagle, B., Olsen, S., Rödl, V. et al. On the Ramsey Number of Sparse 3-Graphs. Graphs and Combinatorics 24, 205–228 (2008). https://doi.org/10.1007/s00373-008-0784-x

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  • DOI: https://doi.org/10.1007/s00373-008-0784-x

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