Counterexamples in percolation: the site percolation critical probabilities pHand pTare unequal for a class of fully triangulated graphs

A family of fully triangulated graphs is given, for which the critical percolation probabilities p T and p H are unequal, and the clusters-per-site function considered by Sykes and Essam (1964) is a polynomial. The graphs are modifications of an example of Van den Berg (1981).