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.
Original language | English |
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Article number | 1850048 |
Journal | Journal of Knot Theory and its Ramifications |
Volume | 27 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2018 Jul 1 |
Bibliographical note
Funding Information:Seungsang Oh was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP) (No. NRF-2017R1A2B2007216).
Publisher Copyright:
© 2018 World Scientific Publishing Company.
Keywords
- Graph
- lattice stick number
- upper bound
ASJC Scopus subject areas
- Algebra and Number Theory