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The classical Ramsey number r(m,n) can be defined as the smallest integer p such that in every two-coloring (R,B) of the edges of K p , β(B)>=m or β(R)>=n, where β(G) denotes the independence number of a graph G. We define the upper domination Ramsey number u(m,n) as the smallest integer p such that in every two-coloring (R,B) of the edges of K p , Γ(B)>=m or Γ(R)>=n, where...
Let G 1 ,G 2 ,…,G t be an arbitrary t-edge colouring of K n , where for each i∈{1,2,…,t}, G i is the spanning subgraph of K n consisting of all edges coloured with colour i. The upper domination Ramsey number u(n 1 ,n 2 ,…,n t ) is defined as the smallest n such that for every t-edge colouring G 1 ,G 2 ,…,G ...
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