### Abstract

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 language | English |
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Article number | 1350003 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 Feb 1 |

### Keywords

- Immersed graph
- chord diagram
- knot
- plane curve

### ASJC Scopus subject areas

- Algebra and Number Theory

## Fingerprint Dive into the research topics of 'Plane curves in an immersed graph in R<sup>2</sup>'. Together they form a unique fingerprint.

## Cite this

Sakamoto, M., & Taniyama, K. (2013). Plane curves in an immersed graph in R

^{2}.*Journal of Knot Theory and its Ramifications*,*22*(2), [1350003]. https://doi.org/10.1142/S021821651350003X