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.
|Journal||Journal of Knot Theory and its Ramifications|
|Publication status||Published - 2018 Jul 1|
- lattice stick number
- upper bound
ASJC Scopus subject areas
- Algebra and Number Theory