Induction formule d'Euler

[capa57]

Finish the proof by induction started during the lecture about Euler's
formula:
For all graphs of e edges, which are planar and connected P(e) : r = e - v + z.

je suis perdu si quelqu'un peut m'aider

En cours on a vu ça... il faut le finir mais comment faire ?

Theorem : For all graphs of e edges, which are planar and connected
P( e ) = r = e-v+2
Proof
Base case
P(1)
E=1
V=2
R=1
1=1-2+2
1=1

Induction step
Assume P( e ) holds

Take on arbitrary connected planar graph of e+1 edges

We use proof by cases :

Case1: remove edge and merges regions
Case2: remove edge and remove node