Published online by Cambridge University Press: 14 August 2020
Erdős, Gyárfás and Pyber showed that every r-edge-coloured complete graph Kn can be covered by 25 r2 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
$p = p(n) = \Omega(n^{-1/(2r)})$
, then with high probability any r-edge-coloured G(n, p) can be covered by at most 1000r4 log r vertex-disjoint monochromatic cycles. This answers a question of Korándi, Mousset, Nenadov, Škorić and Sudakov.
The research leading to these results was supported by EPSRC, grant EP/P002420/1.
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