Exact critical condition for a site-diluted Potts model

The exact phase boundary for a site-diluted q-state Potts model on the honeycomb lattice with vacancies appearing on one of the sublattices only is derived from a duality argument. While the result offers a partial test of recent renormalisation group calculations, it is pointed out that the RG flow structure in this model must be different from that discovered by Nienhuis et al. (see J. Phys. A, vol.13, p.L31, 1980) in fully dilute models, in that for q=2, where our model is exactly solvable, the transition is always second order and it is argued that due to the restriction imposed upon the vacancies this remains so up to q=4.