Global forcing set

Global forcing set --- глобальное вынуждающее множество.

Any set [math]\displaystyle{ S \subseteq E(G) }[/math], such that the restriction of [math]\displaystyle{ f: = {\mathcal M}(G) \rightarrow [0,1]^{|E(G)|} }[/math] on [math]\displaystyle{ S }[/math] is an injection, is called a global forcing set of [math]\displaystyle{ G }[/math]. A global forcing set of the smallest cardinality is called a minimal global forcing set, and its cardinality is a global forcing number of [math]\displaystyle{ G }[/math]. For a given graph [math]\displaystyle{ G }[/math], we denoted its global forcing number by [math]\displaystyle{ \varphi_{g}(G) }[/math].