Ramsey-goodness—and otherwise

@article{Allen2013RamseygoodnessandO,
  title={Ramsey-goodness—and otherwise},
  author={P. Allen and G. Brightwell and J. Skokan},
  journal={Combinatorica},
  year={2013},
  volume={33},
  pages={125-160}
}
  • P. Allen, G. Brightwell, J. Skokan
  • Published 2013
  • Mathematics, Computer Science
  • Combinatorica
  • A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened form) that, for every natural number Δ, there is a constant rΔ such that, for any connected n-vertex graph G with maximum degree Δ, the Ramsey number R(G,G) is at most rΔn, provided n is sufficiently large.In 1987, Burr made a strong conjecture implying that one may take rΔ = Δ. However, Graham, Rödl and Ruciński showed, by taking G to be a suitable expander graph, that necessarily rΔ > 2cΔ for some… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 80 REFERENCES
    On graphs with linear Ramsey numbers
    • 23
    On two problems in graph Ramsey theory
    • 43
    • PDF
    Generalizations of a Ramsey-theoretic result of chvátal
    • 63
    • Highly Influential
    • PDF
    The 3-colored Ramsey number of odd cycles
    • 54
    • PDF
    Generalized Ramsey theory for graphs
    • 163
    • PDF
    Graphs with Linearly Bounded Ramsey Numbers
    • 92
    • PDF
    ON MAXIMAL PATHS AND CIRCUITS OF GRAPHS
    • 165
    • PDF
    The Ramsey number of a graph with bounded maximum degree
    • 167
    • PDF
    Ramsey Numbers for Cycles in Graphs
    • 140
    • PDF
    Every Planar Map Is Four Colorable
    • 1,194
    • PDF