6 problems

Let $G$ be a $2$-tree, meaning that $G$ is obtained recursively from $K_3$ by repeatedly adding a vertex adjacent to two pairwise adjacent existing vertices. Let…

Let $G$ be a 2-tree, that is, a graph obtained from a triangle by repeatedly adding a new vertex adjacent to both endpoints of an existing edge. Let $\mu_{\operatorname{int}}(G)$ d…

Let $G$ be a directed acyclic $2$-tree, and let $\operatorname{sn}(G)$ denote its stack number. Bekos et al.'s conjecture. The stack number of all directed acyclic $2$-trees is bou…

Let $G$ be a $2$-tree of order $n\geq 3$, and let $\bar{\kappa}_{\max}(G)$ denote the maximum, over all orientations of $G$, of the average vertex connectivity of the resulting ori…

Zeng and Yin's conjecture. If $k\ge 3$ with $k\equiv i\pmod 3$, $n$ is sufficiently large, and $\pi\in GS_n$ satisfies

Let $G$ be a linear 2-tree, and let its diameter tend to infinity. Let the maximal resistance distance of $G$ mean the maximum of $r_G(u,v)$ over pairs of vertices. Unbounded resis…