Topological aspects of theta-curves in cubic lattice

Sungjong No, Seungsang Oh, Hyungkee Yoo

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Article number455204
JournalJournal of Physics A: Mathematical and Theoretical
Issue number45
Publication statusPublished - 2021 Nov 12


  • Brunnian
  • lattice stick number
  • theta curve

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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