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Graphs and Combinatorics

, Volume 24, Issue 3, pp 205–228 | Cite as

On the Ramsey Number of Sparse 3-Graphs

  • Brendan Nagle
  • Sayaka Olsen
  • Vojtěch Rödl
  • Mathias SchachtEmail author
Article

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.

Keywords

Ramsey theory hypergraphs Burr–Erdős conjecture 

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Copyright information

© Springer Japan 2008

Authors and Affiliations

  • Brendan Nagle
    • 1
  • Sayaka Olsen
    • 2
  • Vojtěch Rödl
    • 3
  • Mathias Schacht
    • 4
    Email author
  1. 1.Department of MathematicsUniversity of South FloridaTampaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of NevadaRenoUSA
  3. 3.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  4. 4.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany

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