Stick number of spatial graphs

Author:

Lee Minjung1,No Sungjong2,Oh Seungsang1

Affiliation:

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

2. Department of Statistics, Ewha Womans University, Seoul 03760, Korea

Abstract

For a nontrivial knot [Formula: see text], Negami found an upper bound on the stick number [Formula: see text] in terms of its crossing number [Formula: see text] which is [Formula: see text]. Later, Huh and Oh utilized the arc index [Formula: see text] to present a more precise upper bound [Formula: see text]. Furthermore, Kim, No and Oh found an upper bound on the equilateral stick number [Formula: see text] as follows; [Formula: see text]. As a sequel to this research program, we similarly define the stick number [Formula: see text] and the equilateral stick number [Formula: see text] of a spatial graph [Formula: see text], and present their upper bounds as follows; [Formula: see text] [Formula: see text] where [Formula: see text] and [Formula: see text] are the number of edges and vertices of [Formula: see text], respectively, [Formula: see text] is the number of bouquet cut-components, and [Formula: see text] is the number of non-splittable components.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 5 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. Planar Stick Indices of Some Knotted Graphs;Experimental Mathematics;2024-08

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

3. The stick number of rail arcs;Journal of Knot Theory and Its Ramifications;2023-04

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5. Lattice stick number of spatial graphs;Journal of Knot Theory and Its Ramifications;2018-07

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