Let $G_{n,p}^{[\kappa]}$ denote the space of $n$-vertex edge coloured graphs, where each edge occurs independently with probability $p$. The colour of each existing edge is chosen independently and uniformly at random from the set $[\kappa]$. We consider the threshold for the existence of rainbow colored copies of a spanning subgraph $H$. We provide lower bounds on $p$ and $\kappa$ sufficient to prove the existence of such copies w.h.p.

翻译：令 $G_{n,p}^{[\kappa]}$ 表示 $n$ 个顶点的边着色图空间，其中每条边以概率 $p$ 独立出现。每条存在边的颜色从集合 $[\kappa]$ 中独立且均匀地随机选择。我们考虑存在生成子图 $H$ 的彩虹色副本的阈值。我们给出了关于 $p$ 和 $\kappa$ 的下界，这些下界足以以高概率证明此类副本的存在。