2-Irreducibility of spatial graphs

Fengchun Lei*, Kouki Taniyama, Gengyu Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An embedded graph G in the 3-sphere S3 is called 2-irreducible if there are no separating spheres, cutting spheres, singular separating spheres, singular cutting spheres or 2-cutting spheres of G. Let D be a 2-disk in S3 that is very good for G. Let G' be an embedded graph in S 3 obtained from G by contracting D to a point. We show that if G' is 2-irreducible then G is 2-irreducible. By this criterion certain graphs are easily shown to be 2-irreducible. As an application we show a pair of embedded graphs in the 3-sphere which is distinguished by 2-irreducibility.

Original languageEnglish
Pages (from-to)31-41
Number of pages11
JournalJournal of Knot Theory and its Ramifications
Issue number1
Publication statusPublished - 2006 Jan


  • Irreducibility of spatial graph
  • Spatial graph

ASJC Scopus subject areas

  • Algebra and Number Theory


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