8 papers
Lower bounds for the warping degree of a knot projection
Atsushi Ohya, Ayaka Shimizu
The warping degree of an oriented knot diagram is the minimal number of crossings which we meet as an under-crossing first when we travel along the diagram from a fixed point. The…
Unknottability of spatial graphs by region crossing changes
Yukari Funakoshi, Kenta Noguchi, Ayaka Shimizu
A region crossing change is a local transformation on spatial graph diagrams switching the over/under relations at all the crossings on the boundary of a region. In this paper, we…
Prime alternating knots of minimal warping degree two
Ayaka Shimizu
The warping degree of an oriented knot diagram is the minimal number of crossing changes which are required to obtain a monotone knot diagram from the diagram. The minimal warping…
Region crossing change on spatial theta-curves
Ayaka Shimizu, Rinno Takahashi
A region crossing change at a region of a spatial-graph diagram is a transformation changing every crossing on the boundary of the region. In this paper, it is shown that every spa…
On the warping sum of knots
Slavik Jablan, Ayaka Shimizu
The warping sum of a knot is the minimal value of the sum of the warping degrees of a minimal diagram of with both orientations. In this paper, knots with $e(K)…
Up-down colorings of virtual-link diagrams and the necessity of Reidemeister moves of type II
Kanako Oshiro, Ayaka Shimizu, Yoshiro Yaguchi
We introduce an up-down coloring of a virtual-link diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between tw…