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Augmenting the connectivity of geometric graphs. (English) Zbl 1147.05308
Summary: Let $$G$$ be a connected plane geometric graph with $$n$$ vertices. In this paper, we study bounds on the number of edges required to be added to $$G$$ to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for $$G$$ to become 2-edge connected, $$\frac {2n}{3}$$ additional edges are required in some cases and that $$\frac {6n}{7}$$ additional edges are always sufficient. For the special case of plane geometric trees, these bounds decrease to $$\frac{n}{2}$$ and $$\frac{2n}{3}$$, respectively.

##### MSC:
 05C85 Graph algorithms (graph-theoretic aspects) 05C40 Connectivity
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##### References:
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