λ-unknotting-number-one knots need not be prime
Nikos Askitas · Journal of Knot Theory and Its Ramifications · 1999
We show that for certain unknotting operations λ their unknotting number uλ is not additive with respect to connected sums. In general the unknotting number of the connected sum of two knots is smaller than or equal to the sum of the unknotting numbers of the summands; we provide examples where the inequality is strict.