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Lemma: Handshaking Lemma for Planar Graphs

Let $G(V,E)$ be a biconnected planar graph with a given planar drawing $\mathcal D.$ Then the sum of face degrees in the drawing is equal to twice the number of edges, formally

$$\sum_{f\in \mathcal D}\deg (f)=2\cdot|E|.$$

Table of Contents

Proofs: 1

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Proofs: 1 2

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References

Bibliography

  1. Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000