K-Saturated graph

[math]\displaystyle{ k }[/math]-Saturated graph --- [math]\displaystyle{ k }[/math]-насыщенный граф.

A graph [math]\displaystyle{ G }[/math] is [math]\displaystyle{ k }[/math]-saturated, if [math]\displaystyle{ G }[/math] is [math]\displaystyle{ K_{k} }[/math]-free, [math]\displaystyle{ k \geq 3 }[/math], and adding any new edge [math]\displaystyle{ e }[/math] to [math]\displaystyle{ G }[/math] creates a copy [math]\displaystyle{ K_{k} }[/math].