Minor of a graph

Minor of a graph --- минор графа.

A graph [math]\displaystyle{ H }[/math] obtained from [math]\displaystyle{ G }[/math] by a series of vertex deletions, edge deletions and contractions of an edge. A class of graphs [math]\displaystyle{ {\mathcal F} }[/math] is called minor-closed if for every graph [math]\displaystyle{ G }[/math] in [math]\displaystyle{ {\mathcal F} }[/math], every minor of [math]\displaystyle{ G }[/math] is also a member of [math]\displaystyle{ {\mathcal F} }[/math]. For a class of graphs [math]\displaystyle{ {\mathcal F} }[/math], a finite obstruction set [math]\displaystyle{ S }[/math] is a finite set of minors such that a graph is a member of [math]\displaystyle{ {\mathcal F} }[/math] if and only if it does not contain an element of [math]\displaystyle{ S }[/math] as a minor.

The graphs in every minor-closed class of graphs are recognizable in [math]\displaystyle{ {\mathcal O}(n^{3}) }[/math] time.