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Let $G=(V,E)$ be a connected planar graph. This graph has an Euler characteristic given by $\chi=v-e+f$, where $v$ is the number of vertices, $e$ the number of edges and $f$ the number of faces.

I know that $\chi$ is a non-negative integer, but I was wondering which values $\chi$ can assume. Is it possible to determine some bounds on $\chi$?

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