2018/06/25 by Hyungkee Yoo, Yoo, Hyungkee, Chaeryn Lee +3
Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1806.09720
openalex publication_date 2018/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.