Linear component

Linear component --- линейная компонента.

A linear component of a cf-graph [math]\displaystyle{ G }[/math] with the initial node [math]\displaystyle{ p_0 }[/math] and the terminal node [math]\displaystyle{ q_0 }[/math] is defined as a hammock [math]\displaystyle{ C }[/math] such that the following properties hold:

(1) the initial and terminal (if it exists) nodes of [math]\displaystyle{ C }[/math] belongs to every path in [math]\displaystyle{ G }[/math] from [math]\displaystyle{ p_0 }[/math] to [math]\displaystyle{ q_0 }[/math],

(2) the initial node of [math]\displaystyle{ C }[/math] is not reachable in [math]\displaystyle{ G }[/math] from the terminal node of [math]\displaystyle{ C }[/math],

(3) there is no proper subfragment [math]\displaystyle{ A }[/math] of [math]\displaystyle{ C }[/math] such that [math]\displaystyle{ A }[/math] is a hammock and have the first two properties.