A bound for multicolor Ramsey numbers

The Ramsey number R(G1, G2, …, Gn) is the smallest integer p such that for any n-edge coloring (E1,E2, …, En) of Kp, Kp[Ei] contains Gi for some i, Gi as a subgraph in Kp[Ei]. Let R(m1,m2, …, mn)≔R(Km1,Km2, …, Kmn),R(m;n)≔R(m1,m2,…,mn) if mi=m for i=1, 2,…,n. A formula is obtained for R(G1,G2, …, Gn).