Graph Theory: Find a $K_{3,3}$ subdivision to this graph

Question

This is my first post here, so I apologise in advance if some formatting is wrong.

In my graph theory class today we were challenged to find a $K_{3,3}$ (complete bipartite graph) homeomorphic to this .

I've tried to redraw, subdivide edges, and smooth some out, but I can't seem to find it. I'd appreciate any guidance or hints regarding which part to look at.

Answer 1

Let $\{h,e,b\}$ be set 1, and $\{c,g,a\}$ be set 2.

• $b$ is directly connected to $c,g$ and $a$.
  
• $e$ is directly connected to $g$ and $a$, and is connected to $c$ via $d$.
  
• $h$ is directly connected to $c$ and $g$, and is connected to $a$ via $f$.

Answer 2

Try $\{\,a,c,g\,\}$ with $\{\,b,e,h\,\}$.