Anti-Ramsey Numbers of Graphs with Small Connected Components

The anti-Ramsey number, AR(n, G), for a graph G and an integer (Formula presented.) , is defined to be the minimal integer r such that in any edge-colouring of (Formula presented.) 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 (Formula presented.) and (Formula presented.) 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 (Formula presented.) for any (Formula presented.) and (Formula presented.) for any (Formula presented.) for any (Formula presented.) for any (Formula presented.) , and (Formula presented.) for any (Formula presented.). Furthermore, we obtain upper and lower bounds for AR(n, G), for large enough n, where G is (Formula presented.) and (Formula presented.) for any (Formula presented.).