5 problems

Let $\mathbb{D}$ be a P-stable family of degree sequences, or a P-stable simple region, and let $\partial(D)$ denote the boundary of a graphic degree sequence $D\in\mathbb{D}$. Let…

Let $D_1\ge\dotsb\ge D_n$ be a uniformly random graphic sequence of length $n$. The scaling-limit conjecture. There exists a random continuous function $D:[0,1]\to\mathbb{R}$ such…

Monotonicity conjecture. For $n\ge 8$, both sequences

Limiting-ratio conjecture. Both ratios

Asymptotic proportion conjecture.