Delta-Unknotting Number For Pretzel Knots

The [Formula: see text]-unknotting number for a knot is defined as the minimum number of [Formula: see text]-moves needed to deform the knot into the trivial knot. It is known that, for positive pretzel knots, the [Formula: see text]-unknotting number coincides with the second coefficient of their Conway polynomial. In this paper, we compute the [Formula: see text]-unknotting number for positive pretzel knots. As a consequence of the above result, among positive pretzel knots of odd type with a fixed crossing number [Formula: see text], where [Formula: see text] is odd, the [Formula: see text]-unknotting number is maximized by [Formula: see text], and the maximum value is [Formula: see text]. We also obtain a similar result for torus knots. We further determine the [Formula: see text]-unknotting number for pretzel knots of type [Formula: see text], where [Formula: see text] is a positive odd integer for [Formula: see text] and [Formula: see text] is odd.