  The conditions that a planet must fulfill to be habitable are not precisely
known. However, it is comparatively easier to define conditions under which a
planet is very likely not habitable. Finding such conditions is important as it
can help select, in an ensemble of potentially observable planets, which ones
should be observed in greater detail for characterization studies. Assuming, as
in the Earth, that the presence of a C-cycle is a necessary condition for
long-term habitability, we derive, as a function of the planetary mass, a
radius above which a planet is likely not habitable. We compute the maximum
radius a planet can have to fulfill two constraints: surface conditions
compatible with the existence of liquid water, and no ice layer at the bottom
of a putative global ocean. We demonstrate that, above a given radius, these
two constraints cannot be met. We compute internal structure models of planets,
using a five-layer model (core, inner mantle, outer mantle, ocean, and
atmosphere), for different masses and composition of the planets (in
particular, the Fe/Si ratio of the planet). Our results show that for planets
in the Super-Earth mass range (1-12 Mearth), the maximum that a planet, with a
composition similar to that of the Earth, can have varies between 1.7 and 2.2
Rearth. This radius is reduced when considering planets with higher Fe/Si
ratios and taking radiation into account when computing the gas envelope
structure. These results can be used to infer, from radius and mass
determinations using high-precision transit observations like those that will
soon be performed by the CHaracterizing ExOPlanet Satellite (CHEOPS), which
planets are very likely not habitable, and therefore which ones should be
considered as best targets for further habitability studies.}
