Anti-Ramsey threshold of cycles

Abstract

For graphs $G$ and $H$, let $G\stackrel{\mathrm{rb}}{⟶}H$ 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 [J. Combin. Theory Ser. B 124 (2017),1-38], we determine the threshold for $G(n,p)\stackrel{\mathrm{rb}}{⟶}{C}_{\ell }$ for cycles $C_{\ell }$ of any given length $\ell \ge 4$.

12 pages. An extended abstract of this work appeared in the proceedings of the X Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)