Ergodicity of the Wang-Swendsen-Kotecky algorithm on several classes of lattices on the torus

We prove the ergodicity of the Wang-Swendsen-Kotecky (WSK) algorithm for the zero-temperature q-state Potts anti ferromagnet on several classes of lattices on the torus. In particular, the WSK algorithm is ergodic for q >= 4 on any quadrangulation of the torus of girth >= 4. It is also ergodic for q >= 5 (resp. q >= 3) on any Eulerian triangulation of the torus such that one sublattice consists of degree-4 vertices while the other two sublattices induce a quadrangulation of girth >= 4 (resp. a bipartite quadrangulation) of the torus. These classes include many lattices of interest in statistical mechanics.