Thời gian: 15h15-16h15 thứ năm, ngày 11/12/2025

Địa điểm: Phòng 507 nhà A6

Tóm tắt: The random coloured graph $G_c(n,p)$ is obtained from the ErdH{o}s-R'{e}nyi binomial random graph $G(n,p)$ by assigning to each edge a colour from a set of $c$ colours independently and uniformly at random. It is not hard to see that, when $c = Theta(n)$, the order of the largest rainbow tree in this model undergoes a phase transition at the critical point $p=frac{1}{n}$. In this talk, we determine the asymptotic order of the largest rainbow tree in the emph{weakly sub- and supercritical regimes}, when $p = frac{1+eps}{n}$ for some $eps=eps(n)$ which satisfies $eps = o(1)$ and $|eps|^3 ntoinfty$. In particular, we show that in both of these regimes with high probability the largest component of $G_c(n,p)$ contains an almost spanning rainbow tree.