  Annular structures in proto-planetary discs, such as gaps and rings, are now
ubiquitously found by high-resolution ALMA observations. Under the hypothesis
that they are opened by planets, in this paper we investigate how the minimum
planet mass needed to open a gap varies across different stellar host masses
and distances from the star. The dependence on the stellar host mass is
particularly interesting because, at least in principle, gap opening around low
mass stars should be possible for lower mass planets, giving us a look into the
young, low mass planet population. Using dusty hydrodynamical simulations, we
find however the opposite behaviour, as a result of the fact that discs around
low mass stars are geometrically thicker: gap opening around low mass stars can
require more massive planets. Depending on the theoretical isochrone employed
to predict the relationship between stellar mass and luminosity, the gap
opening planet mass could also be independent of stellar mass, but in no case
we find that gap opening becomes easier around low mass stars. This would lead
to the expectation of a {\it lower} incidence of such structures in lower mass
stars, since exoplanet surveys show that low mass stars have a lower fraction
of giant planets. More generally, our study enables future imaging observations
as a function of stellar mass to be interpreted using information on the mass
vs. luminosity relations of the observed samples.
