Newly found forbidden graphs for trivializability

Ryo Nikkuni*, Makoto Ozawa, Kouki Taniyama, Yukihiro Tsutsumi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.

Original languageEnglish
Pages (from-to)523-538
Number of pages16
JournalJournal of Knot Theory and its Ramifications
Issue number4
Publication statusPublished - 2005 Jun


  • Knotted projection
  • Spatial graph
  • Trivializable graph

ASJC Scopus subject areas

  • Algebra and Number Theory


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