  In this short note, we show two NP-completeness results regarding the
\emph{simultaneous representation problem}, introduced by Lubiw and Jampani.
The simultaneous representation problem for a given class of intersection
graphs asks if some $k$ graphs can be represented so that every vertex is
represented by the same interval in each representation. We prove that it is
NP-complete to decide this for the class of interval and circular-arc graphs in
the case when $k$ is a part of the input and graphs are not in a sunflower
position.
