  The possibility that neutron stars may contain substantial hyperon
populations has important implications for neutron-star cooling and, through
bulk viscosity, the viability of the r-modes of accreting neutron stars as
sources of persistent gravitational waves. In conjunction with laboratory
measurements of hypernuclei, astronomical observations were used by Glendenning
and Moszkowski [Phys. Rev. Lett. 67, 2414 (1991)] to constrain the properties
of hyperonic equations of state within the framework of relativistic mean-field
theory. We revisit the problem, incorporating recent measurements of high
neutron-star masses and a gravitational redshift. We find that only the
stiffest of the relativistic hyperonic equations of state commonly used in the
literature is compatible with the redshift. However, it is possible to
construct stiffer equations of state within the same framework which produce
the observed redshift while satisfying the experimental constraints on
hypernuclei, and we do this. The stiffness parameter that most affects the
redshift is not the incompressibility but rather the hyperon coupling.
Nonrelativistic potential-based equations of state with hyperons are not
constrained by the redshift, primarily due to a smaller stellar radius.
