The upper domination Ramsey number u(3,3,3) Original Research Article

Let G1,G2,…,Gt be an arbitrary t-edge colouring of Kn, where for each i∈{1,2,…,t}, Gi is the spanning subgraph of Kn consisting of all edges coloured with colour i. The upper domination Ramsey number u(n1,n2,…,nt) is defined as the smallest n such that for every t-edge colouring G1,G2,…,Gt of Kn, there is at least one i∈{1,2,…,t} for which Ḡi has upper domination number at least ni. We show that 13⩽u(3,3,3)⩽14.