Nowhere-zero k-flow

Nowhere-zero [math]\displaystyle{ k }[/math]-flow --- нигде не нулевой [math]\displaystyle{ k }[/math]-поток, везде ненулевой [math]\displaystyle{ k }[/math]-поток.

A graph admits a nowhere-zero [math]\displaystyle{ k }[/math]-flow ([math]\displaystyle{ k }[/math] is an integer [math]\displaystyle{ \geq 2 }[/math]) if its edges can be oriented and labeled by numbers from [math]\displaystyle{ \{\pm1, \ldots, \pm(k-1)\} }[/math] so that for every vertex the sum of the incoming values equals the sum of the outcoming ones. A graph without nowhere-zero [math]\displaystyle{ k }[/math]-flow is called [math]\displaystyle{ k }[/math]-snark. Note that if a graph is a [math]\displaystyle{ k }[/math]-snarks then it is a [math]\displaystyle{ k' }[/math]-snark for any integer [math]\displaystyle{ 2 \leq k' \leq k }[/math]. Very famous is the 5-flow conjecture of W.T.Tutte which says that there are no bridgeless 5-snarks.