K-Wide distance

[math]\displaystyle{ k }[/math]-Wide distance --- [math]\displaystyle{ k }[/math]-широкое расстояние.

For two distinct vertices [math]\displaystyle{ x,y \in V(G) }[/math], the [math]\displaystyle{ k }[/math]-wide distance [math]\displaystyle{ d_{k}(x,y) }[/math] between [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] is the minimum integer [math]\displaystyle{ l }[/math] such that there exist [math]\displaystyle{ k }[/math] vertex-disjoint [math]\displaystyle{ (x,y) }[/math]-chains whose lengths are at most [math]\displaystyle{ l }[/math]. We define [math]\displaystyle{ d_{k}(x,x) = 0. }[/math]