Stick number of spatial graphs

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.