4 problems

The inhomogeneous Erdős–Rényi significance conjecture. The friendship paradox is significant for every $f\in\mathcal F$ and every $\lambda\in(0,\infty)$:

Relative-moment conjecture. A similar statement should hold in general, or at least for a wide class of weights $W$ and scalings $\lambda_n$.

Let $\nu$ denote the limiting branching-process parameter, and let $\nu_n=1+\varepsilon_n$ be the corresponding parameter for the finite graph. In the subcritical regime, $\nu<1$ (…

Let $c>1$ and $-c\leq\delta\leq c$ be constants, and let $obreakkappa{c+ obreakdelta,c- obreakdelta}$ be the two-type kernel defined in the source. **Square-root threshold conject…