Monochromatic trees in random graphs

Abstract

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.

23 pages, second version addresses changes arising from the referee reports and we added a section showing that the main result does not extend straightforwardly to more than two colours

Cited by in corpus (2)

• Monochromatic cycle partitions in random graphs
• Covering $3$-edge-coloured random graphs with monochromatic trees