Given a graph $G=(V,E)$ on $n$ vertices and an assignment of colours to its edges, a set of edges $S \subseteq E$ is said to be rainbow if edges from $S$ have pairwise different colours assigned to them. In this paper, we investigate rainbow spanning trees in randomly coloured random $G_{k-out}$ graphs.

翻译：给定一个$n$个顶点的图$G=(V,E)$及其边的颜色分配，若边集$S \subseteq E$中任意两条边被分配的颜色均不相同，则称$S$为彩虹集。本文研究了随机染色随机$G_{k-out}$图中的彩虹生成树。