On the super additivity of tunnel number of knots

Abstract. In the present paper, we show a necessary and sufficient condition for knots \(K_1, K_2\) in \(S^3\) (with some side condition) to have the super additivity of tunnel number under connected sum, i.e., \(t(K_1 \# K_2) = t(K_1) + t(K_2) + 1\).