2 problems

For integers $d\geq 1$, let $T_d(n,r)$ be the random graph obtained by sampling $n$ random points of the $d$-dimensional torus $(\mathds{R}/\mathds{Z})^d$ and joining two vertices…

Bounded-degree tree universality resilience conjecture. The conclusion of the cited resilience theorem—that the local resilience of $G(n,p)$ with respect to being universal for…