  The embedding is an essential step when calculating on the D-Wave machine. In
this work we show the hardness of the embedding problem for both types of
existing hardware, represented by the Chimera and the Pegasus graphs,
containing unavailable qubits. We construct certain broken Chimera graphs,
where it is hard to find a Hamiltonian cycle. As the Hamiltonian cycle problem
is a special case of the embedding problem, this proves the general complexity
result for the Chimera graphs. By exploiting the subgraph relation between the
Chimera and the Pegasus graphs, the proof is then further extended to the
Pegasus graphs.
