Bicritical graph

Bicritical graph --- бикритический граф. A finite, undirected, connected and simple graph [math]\displaystyle{ G }[/math] is said to be bicritical if [math]\displaystyle{ G - u - v }[/math] has a perfect matching for each pair of vertices [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] in [math]\displaystyle{ G }[/math] such that [math]\displaystyle{ u \neq v }[/math].

Bicritical graphs play a central role in the decomposition theory of graphs in terms of their maximum matchings.