Monochromatic trees in random graphs
Yoshiharu Kohayakawa, Guilherme Oliveira Mota, Mathias Schacht

TL;DR
This paper determines the threshold for a Ramsey-type property in random graphs, where every 2-coloring results in two disjoint monochromatic trees partitioning all vertices.
Contribution
It establishes the exact threshold for the property in two-colorings, advancing understanding of monochromatic tree partitions in random graphs.
Findings
Threshold for the property in two-colorings is identified.
Provides a precise condition for monochromatic tree partitions.
Advances the theory of Ramsey properties 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 : every -colouring of the edge set of yields pairwise vertex disjoint monochromatic trees that partition the whole vertex set of . We determine the threshold for this property for two colours.
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