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 sL(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) sL(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.
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