The irredundant Ramsey number s = s(m,n) [upper domination Ramsey number u = u(m,n), respectively] is the smallest natural number s [u, respectively] such that in any red-blue edge colouring (R,B) of the complete graph of order s [u, respectively], it holds that IR(B) ≥ m or IR(R) ≥ n [Γ(B) ≥ m or Γ(R) ≥ n, respectively], where Γ and IR denote respectively the upper domination number and the ir...

The size-Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2-edge-coloring of H yields a monochromatic copy of G. Size-Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size-Ramsey numbers for k-uniform hypergraphs. Analogous to the graph case, we cons...

The Ramsey number r(H) of a graphH is the smallest number n such that, in any two-colouring of the edges of Kn, there is a monochromatic copy of H . We study the Ramsey number of graphs H with t vertices and density ρ, proving that r(H) ≤ 2 √ ρ . We also investigate some related problems, such as the Ramsey number of graphs with t vertices and maximum degree ρt and the Ramsey number of random g...

We show that several known Ramsey number inequalities can be extended to the setting of r-uniform hypergraphs. In particular, we extend Burr’s results on tree-star Ramsey numbers, providing exact evaluations for certain hypergraph Ramsey numbers. Then we turn our attention to proving a general multicolor hypergraph Ramsey number inequality from which generalizations of results due to Chvátal an...

Tournaments are orientations of the complete graph. The directed Ramsey number R(k) is minimum vertices a tournament must have to be guaranteed contain transitive subtournament size k, which we denote by $$ TT _k$$ . We include computer-assisted proof conjecture Sanchez-Flores in Graphs Combinatorics 14(2), 181–200 (1998), that all _6$$ -free tournaments on 24 and 25 subtournaments ST _{27}$$ ,...