Exactly fourteen intrinsically knotted graphs have 21 edges

Minjung Lee; Hyoungjun Kim; Hwa Jeong Lee; Seungsang Oh

doi:10.2140/agt.2015.15.3305

Exactly fourteen intrinsically knotted graphs have 21 edges

Minjung Lee, Hyoungjun Kim, Hwa Jeong Lee, Seungsang Oh

Department of Mathematics

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

11 Citations (Scopus)

Abstract

Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K₇ and the thirteen graphs obtained from K₇ by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

Original language	English
Pages (from-to)	3305-3322
Number of pages	18
Journal	Algebraic and Geometric Topology
Volume	15
Issue number	6
DOIs	https://doi.org/10.2140/agt.2015.15.3305
Publication status	Published - 2016 Jan 12

Bibliographical note

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© Mathematical Sciences Publishers. All rights reserved.

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2015.15.3305

Cite this

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title = "Exactly fourteen intrinsically knotted graphs have 21 edges",

abstract = "Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.",

author = "Minjung Lee and Hyoungjun Kim and Lee, {Hwa Jeong} and Seungsang Oh",

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AU - Kim, Hyoungjun

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AU - Oh, Seungsang

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Y1 - 2016/1/12

N2 - Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

AB - Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

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U2 - 10.2140/agt.2015.15.3305

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M3 - Article

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JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 6

ER -

Exactly fourteen intrinsically knotted graphs have 21 edges

Abstract

Bibliographical note

ASJC Scopus subject areas

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