Splitting of a vertice

Splitting of a vertice --- расщепление вершины.

For splitting of a vertice [math]\displaystyle{ x }[/math] of a graph [math]\displaystyle{ G }[/math] into vertices [math]\displaystyle{ x_{1}, \ldots, x_{k} }[/math], one needs to remove [math]\displaystyle{ x }[/math] and replace each [math]\displaystyle{ (x,y) }[/math]-edge ([math]\displaystyle{ y \in V(G) - \{x\} }[/math]) by an [math]\displaystyle{ (x,y) }[/math]-edge for exactly one [math]\displaystyle{ i }[/math], [math]\displaystyle{ 1 \leq i \leq k }[/math].