## 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.

Original language | English |
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Article number | 455204 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 54 |

Issue number | 45 |

DOIs | |

Publication status | Published - 2021 Nov 12 |

### Bibliographical note

Publisher Copyright:© 2021 IOP Publishing Ltd.

## Keywords

- Brunnian
- lattice stick number
- theta curve

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy