Light edge

Light edge --- лёгкое ребро.

Let [math]\displaystyle{ \alpha }[/math] denote an average degree, and [math]\displaystyle{ \delta }[/math] denote the minimum degree of a graph. An edge is light if both its endpoints have a degree bounded by a constant depending only on [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \delta }[/math]. A graph is degree-constrained if [math]\displaystyle{ \alpha \lt 2\delta }[/math]. It is known that every degree-constrained graph has a light edge.