Linear vertex arboricity

Linear vertex arboricity --- линейная вершинная древесность.

A subset of [math]\displaystyle{ V(G) }[/math] is called an [math]\displaystyle{ LV }[/math]-set if it induces a linear forest in [math]\displaystyle{ G }[/math]. A partition of [math]\displaystyle{ V }[/math] is called an [math]\displaystyle{ LV }[/math]-partition if every subset in the partition is an [math]\displaystyle{ LV }[/math]-set. Linear vertex arboricity of [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ \rho'(G) }[/math], is the smallest number of subsets into which the vertex set [math]\displaystyle{ V }[/math] can be partitioned so that the partition is an [math]\displaystyle{ LV }[/math]-partition.