TY - JOUR

T1 - Stick number of spatial graphs

AU - Lee, Minjung

AU - No, Sungjong

AU - Oh, Seungsang

N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Graph

KW - stick number

KW - upper bound

UR - http://www.scopus.com/inward/record.url?scp=85035801760&partnerID=8YFLogxK

U2 - 10.1142/S0218216517501000

DO - 10.1142/S0218216517501000

M3 - Article

AN - SCOPUS:85035801760

SN - 0218-2165

VL - 26

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 14

M1 - 1750100

ER -