2 problems

Disjoint-path connectivity conjecture. The maximum number of disjoint paths between any two permutations $\sigma$ and $\rho$ in $G$ equals $\min\{\deg(\sigma),\deg(\rho)\}$. This w…

Kawarabayashi–Ozeki conjecture. There exists a function $f(k,l)$ such that, for every $f(k,l)$-connected graph $G$ and two distinct vertices $s$ and $t$ in $G$, there are $k$ inter…