Lattice stick number of spatial graphs

Author:

Yoo Hyungkee1,Lee Chaeryn2,Oh Seungsang1

Affiliation:

1. Department of Mathematics, Korea University, Seoul 02841, Korea

2. Department of Mathematics, University of Illinois Urbana Champaign, Urbana, IL 61801, USA

Abstract

The lattice stick number of knots is defined to be the minimal number of straight sticks in the cubic lattice required to construct a lattice stick presentation of the knot. We similarly define the lattice stick number [Formula: see text] of spatial graphs [Formula: see text] with vertices of degree at most six (necessary for embedding into the cubic lattice), and present an upper bound in terms of the crossing number [Formula: see text] [Formula: see text] where [Formula: see text] has [Formula: see text] edges, [Formula: see text] vertices, [Formula: see text] cut-components, [Formula: see text] bouquet cut-components, and [Formula: see text] knot components.

Funder

National Research Foundation of Korea

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Topology-based optimization of handcuff graphs on 3D lattice;Physica Scripta;2023-12-14

2. Lattice conformation of theta-curves accompanied with Brunnian property;Journal of Physics A: Mathematical and Theoretical;2022-10-28

3. Topological aspects of theta-curves in cubic lattice*;Journal of Physics A: Mathematical and Theoretical;2021-10-21

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