### 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 (Formula presented.) of spatial graphs (Formula presented.) 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 (Formula presented.) (Formula presented.) where (Formula presented.) has (Formula presented.) edges, (Formula presented.) vertices, (Formula presented.) cut-components, (Formula presented.) bouquet cut-components, and (Formula presented.) knot components.

Original language | English |
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Journal | Journal of Knot Theory and its Ramifications |

DOIs | |

Publication status | Accepted/In press - 2018 Jun 28 |

### Fingerprint

### Keywords

- Graph
- lattice stick number
- upper bound

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Knot Theory and its Ramifications*. https://doi.org/10.1142/S0218216518500487

**Lattice stick number of spatial graphs.** / Yoo, Hyungkee; Lee, Chaeryn; Oh, Seung Sang.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Lattice stick number of spatial graphs

AU - Yoo, Hyungkee

AU - Lee, Chaeryn

AU - Oh, Seung Sang

PY - 2018/6/28

Y1 - 2018/6/28

N2 - 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 (Formula presented.) of spatial graphs (Formula presented.) 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 (Formula presented.) (Formula presented.) where (Formula presented.) has (Formula presented.) edges, (Formula presented.) vertices, (Formula presented.) cut-components, (Formula presented.) bouquet cut-components, and (Formula presented.) knot components.

AB - 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 (Formula presented.) of spatial graphs (Formula presented.) 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 (Formula presented.) (Formula presented.) where (Formula presented.) has (Formula presented.) edges, (Formula presented.) vertices, (Formula presented.) cut-components, (Formula presented.) bouquet cut-components, and (Formula presented.) knot components.

KW - Graph

KW - lattice stick number

KW - upper bound

UR - http://www.scopus.com/inward/record.url?scp=85049130644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049130644&partnerID=8YFLogxK

U2 - 10.1142/S0218216518500487

DO - 10.1142/S0218216518500487

M3 - Article

AN - SCOPUS:85049130644

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

ER -