On intrinsically knotted or completely 3-linked graphs

Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama, Akiko Yamazaki

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link each of whose 2-component sublinks is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of ΔY-exchanges and YΔ-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

Original languageEnglish
Pages (from-to)407-425
Number of pages19
JournalPacific Journal of Mathematics
Volume252
Issue number2
DOIs
Publication statusPublished - 2011 Nov 9

Keywords

  • Intrinsic knottedness
  • Spatial graph
  • YΔ-exchange
  • ΔY-exchange

ASJC Scopus subject areas

  • Mathematics(all)

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