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$[\kappa]$中独立均匀随机选取。我们研究存在生成子图$H$的彩虹着色副本的阈值。我们给出了$p$和$\kappa$的下界，该下界足以以高概率证明此类副本的存在性。