7 problems

Henning–Oellermann–Swart conjecture.

Let $n$, $k$, and $k^{\prime}$ be integers with $n\geq k\geq3$ and $k>k^{\prime}\geq1$, and let $T$ be a tree with order $n$. The Steiner diameter–radius conjecture. … The paper pr…

Sign conjecture. For any tree on $n$ vertices,

Let $T$ be a tree on $n eq 3$ vertices, let $k$ be a positive integer, and let $d4aeT$ be the order-$k$ Steiner distance hypermatrix of $T$, whose $(v1,d7e2,d7e3,d7e4,d7e5,d7e6)$ e…

Let $G$ be a connected graph of order at least $k$, and let $\operatorname{srad}_k(G)$ and $\operatorname{sdiam}_k(G)$ denote its Steiner $k$-radius and Steiner $k$-diameter, respe…

Let $G$ be a connected graph of order $n\geq k$, and let $\mu(G)$ denote its average distance and $\mu_k(G)$ its average Steiner $k$-distance. Dankelmann–Oellermann–Swart conjectur…

Let $C_n^{2k}$ denote the $2k$-th power of the cycle $C_n$. Let $G$ be a $2k$-connected graph of order $n$. Dankelmann–Swart–Oellermann conjecture. … This conjectures that the $2k$…