Our teacher asked us this question : "Prove that a simple, connected, bipartite and planar graph verifies : . From this, find a proof that is not planar."
Proving that isn't hard, but a friend told me that for n=2 (2 vertex), this fails !
Euler's formula :
And than :
That is false !
I tried to read as much as I could about Euler's formula to see if a minimum number of vertex is necessary, but didn't. Unless I am wrong, the proof starts with a single vertex.
Is it simply that what our teacher asked us isn't * always * true or did my friend and I miss something ?