Gallai–Ramsey Numbers for Paths.

For two graphs G and H, the Gallai–Ramsey number gr k (G : H) is defined as the minimum integer n such that any k-edge-coloring of K n must contain either a rainbow copy of G or a monochromatic copy of H. In this paper, we obtain the exact values of gr k (G : H) , where H is a path and G ∈ { K 1 , 3 , P 4 + , P 5 } is a small tree and P 4 + is the graph consisting of P 4 with one extra edge incident with an inner vertex. [ABSTRACT FROM AUTHOR]