planar graphs

Question

Is there any subgraph homoemorphic to K5 present in G1 for the following question?

 Which one of the following graphs is NOT planar?

    
(A) G1   (B) G2   (C) G3   (D) G4

In this question planar drawings( no 2 edges intersect) for G2, G3 and G4 exists, thats why answer should be G1

But I couldn't find any subgraph homoemorphic to K5 in G1 as a graph is non planar iff it contains a subgraph homoemorphic to K₅ or K_3,3...

Answer 1

The graph G1 is isomorphic to K3,3. And K3,3 is not a planar graph.

Comments

it contains subgraph homomorphic to k5 not to k3,3

Answer 2

Though by simple structure modification you can easily identify that G2, G3, G4 are not planer so now the only choice left is G1.

 

If you notice then G1 is isomorphic to K3,3 and hence it is not planer.

Comments

G2 , G3 and G4 are planar