Abstract
For graphs G and H, let G⟶prbH denote the property that for every proper edge colouring of G there is a rainbow copy of H in G. Extending a result of Nenadov, Person, Škorić and Steger (2017), we prove that n−1/m2(Cℓ) is the threshold for G(n,p)⟶prbCℓ when ℓ ≥ 5. Thus our result together with a result of the third author which says that the threshold for G⟶prbC4 is n−3/4 settles the problem of determining the threshold for G⟶prbCℓ for all values of ℓ.
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