Context. The existence of 2 M⊙ pulsars puts very strong constraints on the equation of state (EOS) of neutron stars (NSs) with hyperon cores, which can be satisfied only by special models of hadronic matter. The radius-mass relation for these models is sufficiently specific that it could be subjected to an observational test with future X-ray observatories. Aims. We want to study the impact of the presence of hyperon cores on the radius-mass relation for NS. We aim to find out how, and for which particular stellar mass range, a specific relation R(M), where M is the gravitational mass, and R is the circumferential radius, is associated with the presence of a hyperon core. Methods. We consider a set of 14 theoretical EOS of dense matter, based on the relativistic mean-field approximation, allowing for the presence of hyperons in NSs. We also discuss a recent EOS based on non-relativistic G-matrix theory yielding NSs with hyperonic cores and M> 2M⊙. We seek correlations between R(M) and the stiffness of the EOS below the hyperon threshold needed to pass the 2 M⊙ test. Results. For NS masses 1.0 <M/M⊙< 1.6, we get R> 13 km, because of a very stiff pre-hyperon segment of the EOS. At nuclear density (n0 = 0.16 fm-3), the pressure is significantly higher than a robust upper bound obtained recently using chiral effective field theory. Conclusions. If massive NSs do have a sizable hyperon core, then according to current models the radii for M = 1.0 − 1.6 M⊙ are necessarily >13 km. If, on the contrary, a NS with a radius R(obs)< 12 km is observed in this mass domain, then sizable hyperon cores in NSs, as we model them now, are ruled out. Future X-ray missions with <5% precision for a simultaneous M and R measurement will have the potential to solve the problem with observations of NSs. Irrespective of this observational test, present EOS allowing for hyperons that fulfill condition Mmax> 2 M⊙ yield a pressure at nuclear density that is too high relative to up-to-date microscopic calculations of this quantity.