Stick number of spatial graphs [article]

Minjung Lee, Sungjong No, Seungsang Oh
2018 arXiv   pre-print
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) ≤ 2 c(K). Later, Huh and Oh utilized the arc index α(K) to present a more precise upper bound s(K) ≤3/2 c(K) + 3/2. Furthermore, Kim, No and Oh found an upper bound on the equilateral stick number s_=(K) as follows; s_=(K) ≤ 2 c(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
more » ... aph G, and present their upper bounds as follows; s(G) ≤3/2 c(G) + 2e + 3b/2 -v/2, s_=(G) ≤ 2 c(G) + 2e + 2b - k, 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.
arXiv:1806.09716v1 fatcat:7pbsof2nrffybn4o6cupjblzju