  After the discovery of a 126 GeV state at the LHC it is imperative to
establish whether this particle really is the Higgs boson of the standard
model. The early measurements have not yet pinpointed any of the Higgs
couplings to fermions, the Yukawa couplings of the standard model. In this
paper we study the values of the top-quark-Higgs coupling, $g_{ht\bar{t}}$,
that are still allowed by the one-loop couplings of the Higgs to two gluons or
two photons. We first assume that both the gluon fusion production of the Higgs
and its decay into two photons proceed through loops with standard model
particles only, albeit with an arbitrary top-Higgs coupling. We find that the
current Higgs data still allows for 20% deviations in $g_{ht\bar{t}}$ from its
standard model value. We then investigate the effect of new particles
contributing to the effective one-loop couplings. Specifically we consider a
color octet electroweak doublet extension of the scalar sector and find that in
this case $g_{ht\bar{t}}$ is allowed to deviate by 40% from its standard model
value by the current data.
