Euler's formula for connected planar graphs Euler's formula for connected planar graphs (i.e. a single connected component) states that $v-e+f=2$. State the generalization of Euler's formula for planar graphs with $k$ connected components (where $k\geq1$). 
The correct answer is $v-e+f=1+k$, but I'm not understanding the reasoning behind it. Anyone care to share some insight?

Given k many components you can "connect" it by adding k-1 many edges, say e'=e+(k-1). Then v-e'+f=2 just says v-e-k+1+f=2 or that v-e+f=1+k.
Note that this agrees with the regular connected version where k just equals 1.
