### 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 |
---|---|

Article number | 1350003 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 Feb |

### Fingerprint

### Keywords

- chord diagram
- Immersed graph
- knot
- plane curve

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

^{2}

*Journal of Knot Theory and its Ramifications*,

*22*(2), [1350003]. https://doi.org/10.1142/S021821651350003X

**Plane curves in an immersed graph in R ^{2}
.** / Sakamoto, Marisa; Taniyama, Kouki.

Research output: Contribution to journal › Article

^{2}',

*Journal of Knot Theory and its Ramifications*, vol. 22, no. 2, 1350003. https://doi.org/10.1142/S021821651350003X

^{2}Journal of Knot Theory and its Ramifications. 2013 Feb;22(2). 1350003. https://doi.org/10.1142/S021821651350003X

}

TY - JOUR

T1 - Plane curves in an immersed graph in R2

AU - Sakamoto, Marisa

AU - Taniyama, Kouki

PY - 2013/2

Y1 - 2013/2

N2 - 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.

AB - 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.

KW - chord diagram

KW - Immersed graph

KW - knot

KW - plane curve

UR - http://www.scopus.com/inward/record.url?scp=84874346194&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874346194&partnerID=8YFLogxK

U2 - 10.1142/S021821651350003X

DO - 10.1142/S021821651350003X

M3 - Article

AN - SCOPUS:84874346194

VL - 22

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 2

M1 - 1350003

ER -