For a fixed graph $F$, the $\textit{anti-Ramsey number}$, $AR(n,F)$, is the maximum number of colors in an edge-coloring of $K_n$ which does not contain a rainbow copy of $F$. In this paper, we determine the exact value of anti-Ramsey numbers of linear forests for sufficiently large $n$, and show the extremal edge-colored graphs. This answers a question of Fang, Győri, Lu and Xiao.

中文翻译：

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关于线性森林的反拉姆齐数

对于固定图 $F$，$\textit{anti-Ramsey number}$，$AR(n,F)$，是 $K_n$ 的边着色中不包含彩虹的最大颜色数$F$ 的副本。在本文中，我们为足够大的 $n$ 确定线性森林的反拉姆齐数的确切值，并显示极值边着色图。这回答了方、吉日、卢和肖的问题。