  The value of the internal energy per spin is independent of the strip width
for a certain class of spin systems on two dimensional infinite strips. It is
verified that the Ising model on the kagome lattice belongs to this class
through an exact transfer-matrix calculation of the internal energy for the two
smallest widths. More generally, one can suggest an upper bound for the
critical coupling strength $K_c(q)$ for the $q$-state Potts model from exact
calculations of the internal energy for the two smallest strip widths.
Combining this with the corresponding calculation for the dual lattice and
using an exact duality relation enables us to conjecture the critical coupling
strengths for the three- and four-state Potts models on the kagome lattice. The
values are $K_c(q=3)=1.056~509~426~929~0$ and $K_c(q=4) = 1.149~360~587~229~2$,
and the values can, in principle, be obtained to an arbitrary precision. We
discuss the fact that these values are in the middle of earlier approximate
results and furthermore differ from earlier conjectures for the exact values.
