N-Extendable graph

[math]\displaystyle{ n }[/math]-Extendable graph --- [math]\displaystyle{ n }[/math]-расширяемый граф.

Let [math]\displaystyle{ G }[/math] be a graph on [math]\displaystyle{ v }[/math] vertices and [math]\displaystyle{ n }[/math] be an integer such that [math]\displaystyle{ 0 \leq n \leq (v - 2)/2 }[/math]. Then [math]\displaystyle{ G }[/math] is [math]\displaystyle{ n }[/math]-extendable if every matching of size [math]\displaystyle{ n }[/math] in [math]\displaystyle{ G }[/math] is contained in a perfect matching of [math]\displaystyle{ G }[/math]. Every [math]\displaystyle{ n }[/math]-extendable graph is also [math]\displaystyle{ (n-1) }[/math]-extendable and also any [math]\displaystyle{ 2 }[/math]-extendable graph is either [math]\displaystyle{ 1 }[/math]-extendable bipartite or bicritical.