Lattice stick number of spatial graphs

Hyungkee Yoo, Chaeryn Lee, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number1850048
JournalJournal of Knot Theory and its Ramifications
Volume27
Issue number8
DOIs
Publication statusPublished - 2018 Jul 1

Keywords

  • Graph
  • lattice stick number
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory

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