Stick number of spatial graphs
- Authors
- Lee, Minjung; No, Sungjong; Oh, Seungsang
- Issue Date
- 12월-2017
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Graph; stick number; upper bound
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.26, no.14
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 26
- Number
- 14
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/81355
- DOI
- 10.1142/S0218216517501000
- ISSN
- 0218-2165
- Abstract
- For a nontrivial knot K, Negami found an upper bound on the stick number s(K) in terms of its crossing number c(K) which is s(K) <= 2c(K). Later, Huh and Oh utilized the arc index a(K) to present a more precise upper bound s(K) <= 3/2 c(K)+3/2. Furthermore, Kim, No and Oh found an upper bound on the equilateral stick number s=(K) as follows; s=(K) <= 2c(K) + 2. As a sequel to this research program, we similarly define the stick number s(G) and the equilateral stick number s=(G) of a spatial graph G, and present their upper bounds as follows; s(G) <= 3/2 c(G) + 2e + 3b/2-v/2, s=(G) <= 2c(G) + 2e + 2b-k, where e and v are the number of edges and vertices of G, respectively, b is the number of bouquet cut-components, and k is the number of non-splittable components.
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