Removing cycle from the complete graph.

Question

How can I remove $6-length$ cycle from the $K_6$ complete graph so that it'll result a $K_{3,3}$ bipartite graph?
I've tried a couple of ways, but I can't get needed result. Maybe this decomposition is impossible?

Thanks in advance.

Answer 1

Try working it backwards: can you draw $K_{3,3}$, then add the missing edges to get $K_6$, with the missing edges forming a $6$-cycle? Answer: no, because the missing edges must form two $3$-cycles.