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Euler formula for a connected planar graph

For a connected planar graph with

n

vertices,

e

edges, and

f

faces,

n - e + f = 2.

Deleting a cycle edge preserves connectedness and decreases both

e

and

f

by one, reducing the formula to its immediate tree case.

Table of contents 71 2
- Planar graph edge bound Euler formula for a connected planar graph 12
- Planar girth edge bound Euler formula for a connected planar graph 23

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