Light graph

Light graph --- лёгкий граф.

A graph [math]\displaystyle{ H }[/math] is defined to be light in a family [math]\displaystyle{ {\mathcal H} }[/math] of graphs if there exists a finite number [math]\displaystyle{ w(H,{\mathcal H}) }[/math] such that each [math]\displaystyle{ G \in {\mathcal H} }[/math], which contains [math]\displaystyle{ H }[/math] as a subgraph, contains also a subgraph [math]\displaystyle{ K \cong H }[/math] such that the sum of degrees (in [math]\displaystyle{ G }[/math]) of the vertices of [math]\displaystyle{ K }[/math] (that is, the weight of [math]\displaystyle{ K }[/math] in [math]\displaystyle{ G }[/math]) is at most [math]\displaystyle{ w(H,{\mathcal H}) }[/math]. Otherwise, we call the graph heavy.