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We investigate the problem of determining how many monochromatic trees arenecessary to cover the vertices of an edge-coloured random graph. Moreprecisely, we show that for $p\gg n^{-1/6}{(\ln n)}^{1/6}$, in any$3$-edge-colouring of the random graph $G(n,p)$ we can find three monochromatictrees such that their union covers all vertices. This improves, for threecolours, a result of Buci\'c, Kor\'andi and Sudakov.

Covering $3$-edge-coloured random graphs with monochromatic trees