Published online by Cambridge University Press: 16 January 2018
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.
The collaboration of the authors was supported by CAPES/DAAD PROBRAL (Proc. 430/15) and by FAPESP (Proc. 2013/03447-6).
Partially supported by FAPESP (Proc. 2013/03447-6, 2013/07699-0), by CNPq (Proc. 459335/2014-6, 310974/2013-5) and by Project MaCLinC/USP.
Supported by FAPESP (Proc. 2013/11431-2, 2013/20733-2) and partially by CNPq (Proc. 459335/2014-6).