  Physics beyond the standard model (SM) can be parameterized with an effective
Lagrangian that respects the symmetries of the standard model and contains many
operators of dimension six. We consider the subset of these operators that is
responsible for flavor diagonal anomalous color magnetic (CMDM) and electric
(CEDM) dipole couplings between quarks and gluons. Invariance of these
operators under the SM implies that they contribute to Higgs boson production
at the LHC and we study the corresponding constraints that can be placed on
them. For the case of the top-quark we first review constraints from top-quark
pair production and decay, and then compare them to what can be achieved by
studying $t\bar{t}h$ production. We also constrain the corresponding couplings
for $b$-quarks and light quarks by studying $pp \to b\bar{b}h$ and $pp \to hX$
respectively.
