Unknotting numbers and crossing numbers of spatial embeddings of a planar graph

Yuta Akimoto, Kouki Taniyama

Research output: Contribution to journalArticlepeer-review

Abstract

It is known that the unknotting number u(L) of a link L is less than or equal to half the crossing number c(L) of L. We show that there are a planar graph G and its spatial embedding f such that the unknotting number u(f) of f is greater than half the crossing number c(f) of f. We study relations between unknotting number and crossing number of spatial embedding of a planar graph in general.

Original languageEnglish
Article number2050095
JournalJournal of Knot Theory and its Ramifications
Volume29
Issue number14
DOIs
Publication statusPublished - 2020 Dec

Keywords

  • Knot
  • crossing number
  • knotted projection
  • spatial graph
  • trivializable graph
  • unknotting number

ASJC Scopus subject areas

  • Algebra and Number Theory

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