User blog comment:Wythagoras/Graphs/@comment-1605058-20140913123957/@comment-10429372-20140913192209

More precise, I think that:


 * A n-cycle must be changed to an (n+2)-cycle if it is not connected to any other cycles.

That is it.
 * Two fused n-cycls must be changed to an (n+1)-cycle if it is not connected to any other cycles.