Region crossing change on origami and link (Q6611938)

Region crossing change is a local operation defined on link diagrams which switches all the crossing points on the boundary of a region. For knot diagrams, it was proved by the second author that any knot diagram can be transformed into a knot diagram representing the unknot via region crossing changes [\textit{A. Shimizu}, J. Math. Soc. Japan 66, No. 3, 693--708 (2014; Zbl 1297.57021)]. In the paper under review, the authors investigate the effect of region crossing changes on an Origami, a square sheet of paper with some creases after a sequence of foldings. Motivated by this, the authors introduce the notion of circled region unlinking number by adding one more circle to link diagrams. It turns out that every nontrivial link admits a link diagram which has circled region unlinking number one.