Euler's formula for connected planar graphs - Mathematics Stack Exchange
SOLVED: Prove that the converse of theorem 1.33 (If G is a planar graph with n ≥ 3 vertices and q edges, then q ≤ 3n − 6. Furthermore, if equality holds,
Must all simple connected graphs fulfilling Euler's formula be planar? If yes, prove it; otherwise find a counter example. - Quora