Induced path number

Induced path number --- число порождённых путей.

The induced path number [math]\displaystyle{ \rho(G) }[/math] of a graph [math]\displaystyle{ G }[/math] is defined as the minimum number of subsets into which the vertex set [math]\displaystyle{ V(G) }[/math] of [math]\displaystyle{ G }[/math] can be partitioned such that each subset induces a path.

If [math]\displaystyle{ G }[/math] is a graph such that [math]\displaystyle{ \rho(G) = k }[/math] and [math]\displaystyle{ \rho(G - v) = k - 1 }[/math] for every [math]\displaystyle{ v \in V(G) }[/math], then we say that [math]\displaystyle{ G }[/math] is [math]\displaystyle{ k }[/math]-minus-critical.