Rainbow copies of spanning subgraphs

Abstract

Let $G_{n,p}^{[\hat{I}º]}$ 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 $[\hat{I}º]$. We consider the threshold for the existence of rainbow colored copies of a spanning subgraph $H$. We provide lower bounds on $p$ and $\hat{I}º$ sufficient to prove the existence of such copies w.h.p.

There is a major error in the paper. The proof incorrectly estimates the number of colors required to get a rainbow copy. It really only gives a trivial estimate