Plane curves in an immersed graph in R2

Marisa Sakamoto*, Kouki Taniyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane-closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to the plane, the sum of averaged invariants of all Hamiltonian plane curves in it is congruent to one quarter modulo one-half.

Original languageEnglish
Article number1350003
JournalJournal of Knot Theory and its Ramifications
Issue number2
Publication statusPublished - 2013 Feb


  • Immersed graph
  • chord diagram
  • knot
  • plane curve

ASJC Scopus subject areas

  • Algebra and Number Theory


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