Finding a monochromatic subgraph or a rainbow path

For simple graphs G and H, let f(G, H) denote the least integer N such that every coloring of the edges of KN contains either a monochromatic copy of G or a rainbow copy of H. Here we investigate f(G, H) when H = Pk. We show that even if the number of colors is unrestricted when defining f(G, H), the function f(G, Pk), for k = 4 and 5, equals the (k − 2)– coloring diagonal Ramsey number of G.