### Abstract

For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2,n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

Original language | English |
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Pages (from-to) | 877-883 |

Number of pages | 7 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 5 |

Issue number | 6 |

Publication status | Published - 1996 Dec |

Externally published | Yes |

### Fingerprint

### Keywords

- Knot
- Planar graph
- Regular projection

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Knot Theory and its Ramifications*,

*5*(6), 877-883.

**Knot-inevitable projections of planar graphs.** / Taniyama, Kouki; Tsukamoto, Tatsuya.

Research output: Contribution to journal › Article

*Journal of Knot Theory and its Ramifications*, vol. 5, no. 6, pp. 877-883.

}

TY - JOUR

T1 - Knot-inevitable projections of planar graphs

AU - Taniyama, Kouki

AU - Tsukamoto, Tatsuya

PY - 1996/12

Y1 - 1996/12

N2 - For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2,n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

AB - For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2,n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

KW - Knot

KW - Planar graph

KW - Regular projection

UR - http://www.scopus.com/inward/record.url?scp=0039419917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039419917&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 877

EP - 883

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 6

ER -