Abstract
We call a subgraph of an edge-colored graph rainbow, if all of its edges have different colors. The anti-Ramsey number of a graph G in a complete graph Kn, denoted by ar(Kn,G), is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of G. In this paper, we determine the exact value of the anti-Ramsey number for star forests and double stars and the approximate value of the anti-Ramsey number for linear forests.
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