  The detection of GW170817 and its electromagnetic counterparts allows to
constrain the equation of state of dense matter in new and complementary ways.
Very stiff equations of state are ruled out by the upper limit on the average
tidal deformability, $\tilde\Lambda \lesssim 800$, imposed by the detected
gravitational wave signal. A lower limit, $\tilde\Lambda \gtrsim 400$, can also
be extracted by considering the large amount of ejected matter which powers the
kilonova AT2017gfo. By using several microscopic nucleonic equations of state,
we first confirm the existence of a monotonic relation between $R_{1.5}$ (the
radius of the $1.5M_{\odot}$ configuration) and $\tilde\Lambda$. This
translates the limits on $\tilde\Lambda$ into limits on the radius:
$11.8\,\text{km} \lesssim R_{1.5} \lesssim 13.1\,$km. We then show that the
monotonic relation is violated, if a second branch of compact stars composed of
quark matter exists, as in the two-families or the twin-stars scenarios. In
particular, it is possible to fulfill the limits on $\tilde\Lambda$ while
having $R_{1.5}$ significantly smaller than $12\,$km. In both those scenarios
the event GW170817/AT2017gfo originates from the merger of a hadronic star and
a star containing quark matter.
