  The half-integer quantum Hall effect in epitaxial graphene is compared with
high precision to the well known integer effect in a GaAs/AlGaAs
heterostructure. We find no difference between the quantised resistance values
within the relative standard uncertainty of our measurement of $8.7\times
10^{-11}$. The result places new tighter limits on any possible correction
terms to the simple relation $R_{\rm K}=h/e^2$, and also demonstrates that
epitaxial graphene samples are suitable for application as electrical
resistance standards of the highest metrological quality. We discuss the
characterisation of the graphene sample used in this experiment and present the
details of the cryogenic current comparator bridge and associated uncertainty
budget.
