The largest hole in sparse random graphs

We show that for any $d=d(n)$ with $d_0(ϵ)\le d=o(n)$, with high probability, the size of a largest induced cycle in the random graph $G(n,d\mathrm{/}n)$ is $(2\pm ϵ)\frac{n}{d}\log d$. This settles a long-standing open problem in random graph theory.