Anti-Ramsey numbers for vertex-disjoint triangles

An edge-colored graph is called rainbow if all the colors on its edges are distinct. Given a positive integer n and a graph G, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of G. Denote by kC3 the union of k vertex-disjoint copies of C3. In this paper, we determine the anti-Ramsey number ar(n,kC3) for n=3k and n≥2k2−k+2, respectively. When 3k≤n≤2k2−k+2, we give lower and upper bounds for ar(n,kC3).