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Euler's formula for graphs embedded into the sphere

>State and prove Euler's formula about graphs embedded into

R^2

Suppose

G

is a finite connected graph drawn on the surface of a sphere

S^2

. Then the complement

S^2 -G

consists of

F=2-\chi(G)

`faces,' connected regions homeomorphic to open discs.

I am having trouble proving this.

Does the Euler characteristic come into it at all?

Thank you for your help

(edited 8 years ago)

Reply 1

Zacken

Original post by number23

...

You might want to replace all your [\tex] with . :-)

Reply 2

Lord of the Flies

Have not studied any graph theory, but surely a stereographic projection is what you want to use here...

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Euler's formula for graphs embedded into the sphere

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