  In the present paper we derive strong constrains on scalarization in
scalar-Gauss-Bonnet (sGB) gravity using observations of pulsars in close binary
systems. Since scalarized neutron stars carry a nonzero scalar change, they
emit scalar dipole radiation while inspiraling which speeds up the orbital
decay. The observations support the conjecture that such radiation is either
absent or very small for the observed binary pulsars. Using this, we determine
the allowed range of parameters for sGB gravity. We also transfer the derived
constraints to black holes in sGB gravity. It turns out that the maximum mass
of a scalarized static black hole can not exceed roughly ten to twenty solar
masses, depending on the initial assumptions we make for the nuclear matter
equations of state. The black hole scalar charge on the other hand can reach
relatively large values that are potentially observable.
