Lattice stick number of spatial graphs

Hyungkee Yoo, Chaeryn Lee, Seung Sang 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 (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 languageEnglish
JournalJournal of Knot Theory and its Ramifications
DOIs
Publication statusAccepted/In press - 2018 Jun 28

Keywords

  • Graph
  • lattice stick number
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory

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