We exhibit a family of 3-uniform hypergraphs with the property that their 2-colour Ramsey numbers grow polynomially in the number of vertices, while their 4-colour Ramsey numbers grow exponentially. This is the first example of a class of hypergraphs whose Ramsey numbers show a strong dependence on the number of colours
We improve upon the lower bound for 3-colour hypergraph Ramsey numbers, showing, in the 3-uniform ca...
Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists...
The Erdos–Hajnal conjecture states that if a graph on n vertices is H-free, that is, it does not con...
We exhibit a family of 3-uniform hypergraphs with the property that their 2-colour Ramsey numbers gr...
Given an r-uniform hypergraph H, the multicolor Ramsey number rk(H) is the minimum n such that every...
Resolving a problem of Conlon, Fox, and R\"{o}dl, we construct a family of hypergraphs with arbitrar...
Let $K_m^{(3)}$ denote the complete $3$-uniform hypergraph on $m$ vertices and $S_n^{(3)}$ the $3$-u...
We show that for all ℓ and ε > 0 there is a constant c = c(ℓ, ε) > 0 such that every ℓ-coloring of t...
Let C(3)n denote the 3-uniform tight cycle, that is, the hypergraph with vertices v1, .–.–., vn and ...
The finite version of Ramsey's theorem says that for positive integers r, k, a_1,... ,a_r, there exi...
The Ramsey number r_(k)(s, n) is the minimum N such that every red-blue coloring of the k-tuples of ...
AbstractLet Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1,...
The induced Ramsey number r_(ind)(F) of a k-uniform hypergraph F is the smallest natural number n fo...
Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists...
A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns an integer from $\{1, \ld...
We improve upon the lower bound for 3-colour hypergraph Ramsey numbers, showing, in the 3-uniform ca...
Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists...
The Erdos–Hajnal conjecture states that if a graph on n vertices is H-free, that is, it does not con...
We exhibit a family of 3-uniform hypergraphs with the property that their 2-colour Ramsey numbers gr...
Given an r-uniform hypergraph H, the multicolor Ramsey number rk(H) is the minimum n such that every...
Resolving a problem of Conlon, Fox, and R\"{o}dl, we construct a family of hypergraphs with arbitrar...
Let $K_m^{(3)}$ denote the complete $3$-uniform hypergraph on $m$ vertices and $S_n^{(3)}$ the $3$-u...
We show that for all ℓ and ε > 0 there is a constant c = c(ℓ, ε) > 0 such that every ℓ-coloring of t...
Let C(3)n denote the 3-uniform tight cycle, that is, the hypergraph with vertices v1, .–.–., vn and ...
The finite version of Ramsey's theorem says that for positive integers r, k, a_1,... ,a_r, there exi...
The Ramsey number r_(k)(s, n) is the minimum N such that every red-blue coloring of the k-tuples of ...
AbstractLet Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1,...
The induced Ramsey number r_(ind)(F) of a k-uniform hypergraph F is the smallest natural number n fo...
Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists...
A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns an integer from $\{1, \ld...
We improve upon the lower bound for 3-colour hypergraph Ramsey numbers, showing, in the 3-uniform ca...
Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists...
The Erdos–Hajnal conjecture states that if a graph on n vertices is H-free, that is, it does not con...
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