Stick number of spatial graphs

Minjung Lee, Sungjong No, Seung Sang Oh

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

For a nontrivial knot K, Negami found an upper bound on the stick number s(K) in terms of its crossing number c(K) which is s(K) ≤ 2c(K). Later, Huh and Oh utilized the arc index α(K) to present a more precise upper bound s(K) ≤ 3/2c(K) + 3/2. Furthermore, Kim, No and Oh found an upper bound on the equilateral stick number s=(K) as follows; s=(K) ≤ 2c(K) + 2. As a sequel to this research program, we similarly define the stick number s(G) and the equilateral stick number s=(G) of a spatial graph G, and present their upper bounds as follows; [Equation presented here] [Equation presented here] where e and v are the number of edges and vertices of G, respectively, b is the number of bouquet cut-components, and k is the number of non-splittable components.

Original languageEnglish
Article number1750100
JournalJournal of Knot Theory and its Ramifications
Volume26
Issue number14
DOIs
Publication statusPublished - 2017 Dec 1

Keywords

  • Graph
  • stick number
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory

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