Stick number of spatial graphs
Minjung Lee, Sungjong No, Seungsang Oh

TL;DR
This paper extends bounds on stick numbers from knots to spatial graphs, providing new upper bounds based on crossing number, edges, vertices, and component counts, advancing understanding of spatial graph complexity.
Contribution
It introduces definitions of stick number and equilateral stick number for spatial graphs and establishes their upper bounds, generalizing previous knot results.
Findings
Derived upper bounds for stick number of spatial graphs
Established bounds depend on crossing number, edges, and vertices
Generalized knot bounds to spatial graphs
Abstract
For a nontrivial knot , Negami found an upper bound on the stick number in terms of its crossing number which is . Later, Huh and Oh utilized the arc index to present a more precise upper bound . Furthermore, Kim, No and Oh found an upper bound on the equilateral stick number as follows; . As a sequel to this research program, we similarly define the stick number and the equilateral stick number of a spatial graph , and present their upper bounds as follows; where and are the number of edges and vertices of , respectively, is the number of bouquet cut-components, and is the number of non-splittable components.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · graph theory and CDMA systems
