10 problems

Let $X$ denote the limiting random variable associated with the normalized maximum degree in Theorem 1.2, and let $D_1$ and $D_2$ be the constants appearing there. Maximum-degree l…

Degree-distribution conjecture. The ratio

Let $\mathcal{T}$ be a $(\mu,f,\ell)$-RIF tree, and define … Assume that $\alpha=\infty$, and let $N_0(t,B)$ denote the number of degree-zero vertices present by time $t$ whose fit…

Let $\mathcal{T}$ be a $(\mu,f,\ell)$-RIF tree, and define … For $\alpha<\infty$, let $N_k(t,B)$ denote the number of degree-$k$ vertices present by time $t$ whose fitness lies in…

Let the Erlang Weighted Tree have a root vertex and generations indexed by $l$, and let the degree distribution of the $l$th generation be the distribution of vertex degrees in tha…

Let $m\in\mathbb{N}$, let $G_t$ be a graph in Regime $R2$, and let $\mathbf{deg}_t$ be its empirical degree distribution. Let $\mathbf{deg}_t^{BB(m)}$ be the empirical degree distr…

Let $m\in\mathbb{N}$, let $G_t$ be a graph in Regime $R1$, and let $\mathbf{deg}_t$ be its empirical degree distribution. Let $\mathbf{deg}_t^{BA}$ be the empirical degree distribu…

In the meek-choice preferential attachment tree, a new vertex selects $r$ potential neighbours according to the preferential attachment rule and connects to the vertex with the $s$…

Expected second-degree distribution conjecture. For

For each integer $k\geq 1$, let $Z^{(k)}_n$ denote the proportion of vertices of degree $k$ in a uniformly random planar graph with $n$ vertices. Limiting degree-distribution conje…