consider the following language: $HAM-NO-HAM=\{(G_1,G_2)|G_1, G_2\}$ are undirected graphs, $G_1$ has a Hamilton and $G_2$ doesn't have one$\}$.
i need to decide wheter it's in $P, NP, CONP$ or none of the above.
If I'll show reductions from $HAMcircuit$ and from $NO-HAMcircuit$ I will get that $HAM-NO-HAM$ is both $NPC$ and $coNPC$.
What is the best way for showing a reduction from the $HAMcircuit$ to $HAM-NO-HAM$?
I want somehow to copy it and then I would get the graph which does or doesn't have a $HAMcircuit$ but I need to copy it again so it would fit the other other condition for the second graph.
Any suggestion?