Anti-Ramsey Numbers of Graphs with Small Connected Components

The anti-Ramsey number, AR(n, G), for a graph G and an integer , is defined to be the minimal integer r such that in any edge-colouring of by at least r colours there is a multicoloured copy of G, namely, a copy of G that each of its edges has a distinct colour. In this paper we determine, for large enough and for any large enough t and k, and a graph L satisfying some conditions. Consequently, we determine AR(n, G), for large enough n, where G is for any and for any for any for any , and for any . Furthermore, we obtain upper and lower bounds for AR(n, G), for large enough n, where G is and for any k >= 4, t >= 1.