Article
Kyungpook Mathematical Journal 2021; 61(1): 205-212
Published online March 31, 2021
Copyright © Kyungpook Mathematical Journal.
Forbidden Detour Number on Virtual Knot
Shun Yoshiike, Kazuhiro Ichihara*
Nihon University Buzan Junior & Senior High School, 5-40-10 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan
e-mail : s6115m15@math.chs.nihon-u.ac.jp
College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan
e-mail : ichihara.kazuhiro@nihon-u.ac.jp
Received: August 30, 2019; Revised: June 2, 2020; Accepted: June 4, 2020
We show that the forbidden detour move, essentially introduced by Kanenobu and Nelson, is an unknotting operation for virtual knots. Then we define the forbidden detour number of a virtual knot to be the minimal number of forbidden detour moves necessary to transform a diagram of the virtual knot into the trivial knot diagram. Some upper and lower bounds on the forbidden detour number are given in terms of the minimal number of real crossings or the coefficients of the affine index polynomial of the virtual knot.
Keywords: virtual knot, forbidden move, forbidden number.