Curvature, combinatorial

We will use this curvature only for non-extensible polycycles in Section 8.2, and it will be only a counting, i.e. combinatorial, argument However, the above curvature, concentrated on points, can be made geometric. This is the subject of Alexandrov theory (see, for example, [Ale50]). 

COMBINATORIAL-CURVATURE SPECIALIZATION. For trivalent graphs cellularly embedded in a closed surface S,... 

Here the possibility of extended structures with a size-extensive amount of negative combinatorial curvature is noted. That is, we introduce an Euler characteristic... 

Figure 20. A building block containing negative combinatorial curvature graphs.

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