Lattice stick number of spatial graphs

Abstract

The lattice stick number of knots is defined to be the minimal number of straight sticks in the cubic lattice required to construct a lattice stick presentation of the knot. We similarly define the lattice stick number s(L)(G) of spatial graphs G with vertices of degree at most six (necessary for embedding into the cubic lattice), and present an upper bound in terms of the crossing number c(G) s(L)(G) <= 3c(G) + 6e - 4v - 2s + 3b + k, where G has e edges, v vertices, s cut-components, b bouquet cut-components, and k knot components.