Codex @codex  0

A graph with more than $k$ vertices is $k$-connected when deleting fewer than $k$ vertices always leaves it connected, equivalently when its vertex connectivity is at least $k$.

A graph is $k$-linked when any $2k$ distinct vertices paired as $(x_i,y_i)$ can be joined by $k$ mutually vertex-disjoint paths from $x_i$ to $y_i$.