Off-diagonal hypergraph Ramsey numbers

@article{Mubayi2017OffdiagonalHR,
  title={Off-diagonal hypergraph Ramsey numbers},
  author={Dhruv Mubayi and Andrew Suk},
  journal={J. Comb. Theory, Ser. B},
  year={2017},
  volume={125},
  pages={168-177}
}
  • Dhruv Mubayi, Andrew Suk
  • Published 2017
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • The Ramsey number $r_k(s,n)$ is the minimum $N$ such that every red-blue coloring of the $k$-subsets of $\{1, \ldots, N\}$ contains a red set of size $s$ or a blue set of size $n$, where a set is red (blue) if all of its $k$-subsets are red (blue). A $k$-uniform \emph{tight path} of size $s$, denoted by $P_{s}$, is a set of $s$ vertices $v_1 < \cdots < v_{s}$ in $\mathbb{Z}$, and all $s-k+1$ edges of the form $\{v_j,v_{j+1},\ldots, v_{j + k -1}\}$. Let $r_k(P_s, n)$ be the minimum $N$ such that… CONTINUE READING

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    Constructions in Ramsey theory
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    Variants of the Erdős-Szekeres and Erdős-Hajnal Ramsey problems
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 36 REFERENCES
    Hypergraph Ramsey numbers
    77
    Ramsey Theory
    • Ramsey Theory
    652
    Multicolor Ramsey numbers for triple systems
    16
    The Erdős-Hajnal hypergraph Ramsey problem
    6
    An improved bound for the stepping-up lemma
    30
    Ramsey Theory, integer partitions and a new proof of the Erdős–Szekeres Theorem
    38
    Shift graphs and lower bounds on Ramsey numbers rk(l; r)
    23
    The early evolution of the H-free process
    140
    On Ramsey Like Theorems , Problems and Results
    36
    Combinatorial Theorems on Classifications of Subsets of a Given Set
    195