Seidel's switching is a graph operation which makes a given vertex adjacent
to precisely those vertices to which it was non-adjacent before, while keeping
the rest of the graph unchanged. Two graphs are called switching-equivalent if
one can be made isomorphic to the other one by a sequence of switches.
Jel\'inkov\'a et al. [DMTCS 13, no. 2, 2011] presented a proof that it is
NP-complete to decide if the input graph can be switched to contain at most a
given number of edges. There turns out to be a flaw in their proof. We present
a correct proof.
Furthermore, we prove that the problem remains NP-complete even when
restricted to graphs whose density is bounded from above by an arbitrary fixed
constant. This partially answers a question of Matou\v{s}ek and Wagner
[Discrete Comput. Geom. 52, no. 1, 2014].Comment: 19 pages, 7 figures. An extended abstract submitted to COCOON 201