added qubits we can break the $DT(G)$ in three copies of the same base-graph: one will be used for the computation while the other two can be used as traps. Furthermore for each vertex base-location the choice of where to break the graph is independent from other vertex base-locations and can be made in advance by the client. The server remains totally ignorant of this choice. This choice is called *trap-colouring*.

\[trap colouring\] We define trap-colouring to be an assignment of one colour to each of the vertices of the dotted triple-graph that is consistent with the following conditions:

1.  Primary vertices are coloured in one of the three following colours: white or black (for traps), or green (for computation).

2.  Added vertices are coloured in one of the four following colours: white, black, green or red.

3.  In each primary set $P_v$ there is exactly one vertex of each colour.

4.  Colouring the primary vertices fixes the colours of the added vertices: added vertices that connect primary vertices of different colour are red, added vertices that connect primary vertices of the same colour get that colour.

![Dotted-triple-graph for one-dimensional base graph of four qubits. Circles: primary vertices (base-location : 