Add to ORKGWe provide proofs to check and exposit Exoo's construction of a colouring on $K_{42}$ that demonstrates that $R(5,5)>42$. The proof suggests is also possible to extract from this construction a colouring of $K_{43}$ that has very few monochromatic $K_5$s.Comment: 15 pages, 1 figure, 3 reference
The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of ...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Ramsey Theory states that there exists a Ramsey Number. This number is the minimum number of nodes n...
Resolving a problem of Conlon, Fox, and R\"{o}dl, we construct a family of hypergraphs with arbitrar...
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...
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...
In this article we use two di#erent methods to find new lower bounds for some multicolored Ramsey n...
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed numbe...
This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short ove...
This paper sets out the results of a range of searches for linear and cyclic graph colourings with s...
This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short ove...
AbstractIn this note we obtain new lower bounds for the Ramsey numbers R(5, 5) and R(5, 6). The meth...
AbstractIn this note we obtain a new lower bound for the Ramsey number R(5, 6). The method is comput...
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of ...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Ramsey Theory states that there exists a Ramsey Number. This number is the minimum number of nodes n...
Resolving a problem of Conlon, Fox, and R\"{o}dl, we construct a family of hypergraphs with arbitrar...
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...
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...
In this article we use two di#erent methods to find new lower bounds for some multicolored Ramsey n...
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed numbe...
This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short ove...
This paper sets out the results of a range of searches for linear and cyclic graph colourings with s...
This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short ove...
AbstractIn this note we obtain new lower bounds for the Ramsey numbers R(5, 5) and R(5, 6). The meth...
AbstractIn this note we obtain a new lower bound for the Ramsey number R(5, 6). The method is comput...
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of ...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Ramsey Theory states that there exists a Ramsey Number. This number is the minimum number of nodes n...