Retract

Retract --- ретракт.

A retraction [math]\displaystyle{ f }[/math] from a graph [math]\displaystyle{ H = (V_{H},E_{H}) }[/math] to a subgraph [math]\displaystyle{ G = (V_{G},E_{G}) }[/math] is a mapping [math]\displaystyle{ f: \; V_{H} \rightarrow V_{G} }[/math] such that for every edge [math]\displaystyle{ (u,v) \in E_{H} }[/math] [math]\displaystyle{ (f(u),f(v)) \in E_{G} }[/math] and [math]\displaystyle{ f(w) = w }[/math] for all [math]\displaystyle{ w \in V_{G} }[/math]. Then [math]\displaystyle{ G }[/math] is a retract of [math]\displaystyle{ H }[/math]. [math]\displaystyle{ G }[/math] is an absolute retract if [math]\displaystyle{ G }[/math] is a retract of any graph [math]\displaystyle{ H }[/math] containing [math]\displaystyle{ G }[/math] as an isometric subgraph, provided that [math]\displaystyle{ \chi(G) = \chi(H) }[/math]. Note that a retract [math]\displaystyle{ G }[/math] of [math]\displaystyle{ H }[/math] is necessarily an isometric subgraph of [math]\displaystyle{ H }[/math].