5 problems

Simple optimal solution conjecture. Every instance of MinCRS admits a simple optimal solution.

Hub-separation conjecture. The solutions to the formulation in Eq. $$ would have separated hubs in a bigger network in order to symmetrize other parts of the network connected to t…

Let $H$ be a graph with no isolated vertices, let $k$ be a positive integer, and let $\beta(H,k)$ be the optimization parameter defined in the paper. Attainment conjecture for…

Let $C_m$ be the cycle on $m$ edges, let $E(C_m)$ be its edge set, and let $\beta(C_m,1)$ be the optimization parameter defined in the paper. Uniform-mass conjecture for cycles. Fo…

For an integer $m\geq 2$, let $C_m$ be the cycle on $m$ edges, let $E(C_m)$ be its edge set, and let $\rho(m)$ be the path optimization parameter defined in the paper. Uniform-mass…