Topological aspects of theta-curves in cubic lattice

Sungjong No, Seungsang Oh, Hyungkee Yoo

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    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 languageEnglish
    Article number455204
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume54
    Issue number45
    DOIs
    Publication statusPublished - 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

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