## On Tunnel Number One Alternating Knots and Links

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 3, Page 547--560.

Shimokawa, Koya
On Tunnel Number One Alternating Knots and Links
In this article we consider tunnel number one alternating knots and links. We characterize tunnel number one alternating knots and links which have unknotting tunnels contained in regions of reduced alternating diagrams. We show that such a knot or link is a $2$-bridge or a Montesinos knot or link or the connected sum of the Hopf link and a $2$-bridge knot.