  We theoretically compute the thermal conductivity of SiGe alloy nanowires as
a function of nanowire diameter, alloy concentration, and temperature,
obtaining a satisfactory quantitative agreement with experimental results. Our
results account for the weaker diameter dependence of the thermal conductivity
recently observed in Si$_{1-x}$Ge$_x$ nanowires ($x<0.1$), as compared to pure
Si nanowires. We also present calculations in the full range of alloy
concentrations, $0 \leq x \leq 1$, which may serve as a basis for comparison
with future experiments on high alloy concentration nanowires.
