Monochromatic cycle partitions in random graphs

Erd\H{o}s, Gy'arf'as and Pyber showed that every $r$-edge-coloured complete graph $K_n$ can be covered by $25r^2\log r$ vertex-disjoint monochromatic cycles (independent of $n$). Here, we extend their result to the setting of binomial random graphs. That is, we show that if $p = p(n) = \Omega(n^{-1/(2r)})$,thenwithhighprobabilityany$r$-edge-coloured$G(n,p)$canbecoveredbyatmost$1000 r^4 \log r $ vertex-disjoint monochromatic cycles. This answers a question of Kor'andi, Mousset, Nenadov, \v{S}kori'{c} and Sudakov.