Topological aspects of theta-curves in cubic lattice*
- Authors
- No, Sungjong; Oh, Seungsang; Yoo, Hyungkee
- Issue Date
- 12-11월-2021
- Publisher
- IOP Publishing Ltd
- Keywords
- Brunnian; lattice stick number; theta curve
- Citation
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, v.54, no.45
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Volume
- 54
- Number
- 45
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/135740
- DOI
- 10.1088/1751-8121/ac2ae9
- ISSN
- 1751-8113
- Abstract
- Knots and embedded graphs are useful models for simulating polymer chains. In particular, a theta curve motif is present in a circular protein with internal bridges. A theta-curve is a graph embedded in three-dimensional space which consists of three edges with shared endpoints at two vertices. If we cannot continuously transform a theta-curve into a plane without intersecting its strand during the deformation, then it is said to be nontrivial. A Brunnian theta-curve is a nontrivial theta-curve that becomes a trivial knot if any one edge is removed. In this paper we obtain qualitative results of these theta-curves, using the lattice stick number which is the minimal number of sticks glued end-to-end that are necessary to construct the theta-curve type in the cubic lattice. We present lower bounds of the lattice stick number for nontrivial theta-curves by 14, and Brunnian theta-curves by 15.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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