Gallai–Ramsey numbers for cycles

For given graphs GG and HH and an integer kk, the Gallai–Ramsey number is defined to be the minimum integer nn such that, in any kk coloring of the edges of KnKn, there exists a subgraph isomorphic to either a rainbow coloring of GG or a monochromatic coloring of HH. In this work, we consider Gallai–Ramsey numbers for the case when G=K3G=K3 and HH is a cycle of a fixed length.