Region crossing change on spatial theta-curves
Ayaka Shimizu, Rinno Takahashi
TL;DR
This paper demonstrates that any spatial theta-curve can be unknotted through a sequence of region crossing changes, providing a new method for simplifying complex spatial graphs.
Contribution
It introduces the use of region crossing changes as a technique to unknot spatial theta-curves, expanding the toolkit for spatial graph manipulation.
Findings
Any spatial theta-curve can be unknotted by region crossing changes.
Region crossing change is effective for simplifying spatial theta-curves.
The method provides a new approach for unknotting spatial graphs.
Abstract
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 spatial graph consisting of theta-curves can be unknotted by region crossing changes.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Topological and Geometric Data Analysis · Data Management and Algorithms