# Tunnel number of Pretzel knots

I would like to know the tunnel number of $n$-pretzel knots. I have searched and found nothing for any $n>3$. When $n=2$, $t(K)=1$ or $2$ depending on the number of twists, which is proved in a paper by Morimoto, Sakuma, and Yokota. Does anyone know if this has been computed for $n>3$? I know that Yokota has a paper about estimating tunnel number using quantum invariants, but I am not sure that it will be useful here the whole class of pretzel knots. But if you know that it will be, then it would be great to know that as well. Thanks.

• Hi again Ian. I just found out that Lustig and Moriah have a paper, Generalized Montesinos Knots, tunnels, and N-torsion, which computes the rank and tunnel number of a class of knots which includes Montesinos Knots. For an $n$-Montesinos knot $K$, rank$(\pi_1 (S^3 - K))= t(K)+1=b(K)=n$ – N. Owad Apr 17 '15 at 15:43