Knot-inevitable projections of planar graphs

Kouki Taniyama; Tatsuya Tsukamoto

doi:10.1142/S0218216596000485

Knot-inevitable projections of planar graphs

Kouki Taniyama^*, Tatsuya Tsukamoto

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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
Pages (from-to)	877-883
Number of pages	7
Journal	Journal of Knot Theory and its Ramifications
Volume	5
Issue number	6
DOIs	https://doi.org/10.1142/S0218216596000485
Publication status	Published - 1996 Dec
Externally published	Yes

Keywords

Knot
Planar graph
Regular projection

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1142/S0218216596000485

Cite this

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title = "Knot-inevitable projections of planar graphs",

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.",

keywords = "Knot, Planar graph, Regular projection",

author = "Kouki Taniyama and Tatsuya Tsukamoto",

year = "1996",

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AU - Taniyama, Kouki

AU - Tsukamoto, Tatsuya

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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

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ER -

Knot-inevitable projections of planar graphs

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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