Random tree-weighted graphs

Louigi Addario-Berry, Jordan Barrett

For each $n\ge 1$, let ${\mathrm{d}}^n=(d^n(i),1\le i\le n)$ be a sequence of positive integers with even sum ${\sum }_{i=1}^n{d}^n(i)\ge 2n$. Let $(G_n,T_n,{\Gamma }_n)$ be uniformly dist…