Monochromatic trees in random graphs
  Bal and DeBiasio [Partitioning random graphs into monochromatic components, Electron. J. Combin. 24 (2017), Paper 1.18] put forward a conjecture concerning the threshold for the following Ramsey-type property for graphs $G$: every $k$-colouring of the edge set of $G$ yields $k$ pairwise vertex disjoint monochromatic trees that partition the whole vertex set of $G$. We determine the threshold for this property for two colours. 
Yoshiharu Kohayakawa, Guilherme Oliveira Mota, Mathias Schacht
math.CO