AbstractThe sub-Ramsey number sr(Kn,k) is the smallest integer m such that in any edge-colouring of Km which uses every colour at most k times some subgraph Kn has all edges of different colours. It was known that, for a fixed k, the function sr(Kn,k) is O(n3) and Ω(n). We improve these bounds to O(n2) and Ω(n3/2) (slightly less for small values of k)
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
AbstractSuppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; ...
AbstractThe generalised Ramsey number R(G1, G2,..., Gk) is defined as the smallest integer n such th...
AbstractThe sub-Ramsey number sr(Kn,k) is the smallest integer m such that in any edge-colouring of ...
AbstractWe show the existence of a constant c such that if n ⩾ ck3 and the edges of Kn are coloured ...
AbstractGiven a positive integer n and a family F of graphs, let R∗(n,F) denote the maximum number o...
We prove that $s_r(K_k) = O(k^5 r^{5/2})$, where $s_r(K_k)$ is the Ramsey parameter introduced by Bu...
The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1...
The authors investigate Ramsey-type extremal problems for finite graphs. In Section 1, anti-Ramsey n...
Let c be an edge-colouring of the complete n-graph Kn with m colours. A totally multicoloured (TMC) ...
We determine the Ramsey number of a connected clique matching. That is, we show that if GG is a 22-e...
Fix positive integers p and q with [equation; see abstract in PDF for details]. An edge coloring of...
AbstractClassical Ramsey numbers r=rt(G) ask for the smallest number r such that every t-coloring of...
Fix positive integers p and q with [equation; see abstract in PDF for details]. An edge coloring of...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
AbstractSuppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; ...
AbstractThe generalised Ramsey number R(G1, G2,..., Gk) is defined as the smallest integer n such th...
AbstractThe sub-Ramsey number sr(Kn,k) is the smallest integer m such that in any edge-colouring of ...
AbstractWe show the existence of a constant c such that if n ⩾ ck3 and the edges of Kn are coloured ...
AbstractGiven a positive integer n and a family F of graphs, let R∗(n,F) denote the maximum number o...
We prove that $s_r(K_k) = O(k^5 r^{5/2})$, where $s_r(K_k)$ is the Ramsey parameter introduced by Bu...
The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1...
The authors investigate Ramsey-type extremal problems for finite graphs. In Section 1, anti-Ramsey n...
Let c be an edge-colouring of the complete n-graph Kn with m colours. A totally multicoloured (TMC) ...
We determine the Ramsey number of a connected clique matching. That is, we show that if GG is a 22-e...
Fix positive integers p and q with [equation; see abstract in PDF for details]. An edge coloring of...
AbstractClassical Ramsey numbers r=rt(G) ask for the smallest number r such that every t-coloring of...
Fix positive integers p and q with [equation; see abstract in PDF for details]. An edge coloring of...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
AbstractSuppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; ...
AbstractThe generalised Ramsey number R(G1, G2,..., Gk) is defined as the smallest integer n such th...
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