6 problems

Let $q\geq 1$ and let $d\colon(\mathbb{R}^q)^n\to\mathbb{R}_+$ assign to $(x_1,\ldots,x_n)$ the total length of a minimal spanning tree of the complete Euclidean graph on these poi…

For each integer $n\geq 1$, let $K_n$ be the complete graph on $n$ vertices, and let $L(K_n)$ denote the length of its minimal spanning tree with the edge-weight model used in Stee…

Consider an inhomogeneous random graph model whose limiting degree distribution has finite third moments. In the supercritical regime, form the minimal spanning tree on its giant c…

Let $\mathsf{MST}_\infty$ be a subsequential scaling limit of the minimal spanning tree on the planar lattice, viewed in $\hat{\mathbb{C}}$. A branching point is a point where mult…

Let $\widetilde{RCM}[n]$ be the weighted repeated configuration model on $n$ vertices obtained from a given degree sequence, with independent identically distributed edge lengths.…

Minimal spanning tree diameter conjecture. The diameter of the minimal spanning trees in various random graph models scales like $n^{1/3}$.