Regularity of powers of (parity) binomial edge ideals

In this paper, we provide exact formulas for the regularity of powers of an almost complete intersection ideal I which is generated by a homogeneous d-sequence. As applications, when I is an almost complete intersection, taking the form of a (parity) binomial edge ideal of a connected graph, we can describe explicitly reg(I-t) for t >= 2. The only exception is when I is the parity binomial edge ideal of a graph which is obtained by adding an edge between two disjoint odd cycles.