A note on tunnel number of composite knots

Let K be a knot in a sphere S 3 . We denote by t ( K ) the tunnel number of K. For two knots K 1 and K 2 , we denote by K 1 ♯ K 2 the connected sum of K 1 and K 2 . In this paper, we will prove that if one of K 1 and K 2 has high distance while the other has distance at least 3 then t ( K 1 ♯ K 2 ) = t ( K 1 ) + t ( K 2 ) + 1 .